International Society of Nonlinear Mathematical Physics
  

Book Reviews and Recommendations


The ISNMP Library: Literature Recommendations

The following list consists of books in Nonlinear Mathematical Physics and related subjects, all of which have been recommended by members of the ISNMP. The list is alphabetically orderd according to the authors or editors of the books, and the links are to the publishers where information about the books can be found. 

  • Ablowitz, MJ (author), "Nonlinear Dispersive Waves": Asymptotic Analysis and Solitons, Cambridge University Press, 2011. Link
  • Ablowitz, MJ; Clarkson, PA (authors), "Solitons, Nonlinear Evolution Equations and Inverse Scattering", Cambridge University Press, 1991. Link
  • Ablowitz, MJ; Prinari, B; Trubatch, AD (authors), "Discrete and Continuous Nonlinear Schrödinger Systems", Cambridge University Press, 2003. Link
  • Adler, M; Van Moerbeke, P; Vanhaecke, P (authors), "Algebraic Integrability, Painlevé Geometry and Lie Algebras", Springer, 2004. Link
  • Arnold, VI; Gelfand, IM; Retakh, VS; Smirnov M (editors), "The Arnold-Gelfand Mathematical Seminars", Birkhäuser (available by Springer Nature Link), 1997. Link
  • Arnold, VI; Novikov, SP (editors), "Dynamical Systems IV": Symplectic Geometry and its Applications, Springer , 2001. Link
  • Arutyunov, G (author), "Elements of Classical and Quantum Integrable Systems", Springer, 2019. Link
  • Athorne, C; Maclagan, D; Strachan, I (editors), "Tropical Geometry and Integrable Systems", AMS, 2012. Link
  • Audin, M; Silva, AC; Lerman, E (authors), "Symplectic Geometry of Integrable Hamiltonian Systems", Birkhäuser (available by Springer Nature Link), 2003. Link
  • Babelon, O; Bernard, D; Talon, M (authors), "Introduction to classical integrable systems", Cambridge University Press, 2003. Link
  • Babelon, O; Kosmann-Schwarzbach, Y; Cartier, P (editors), "Integrable Systems": The Verdier Memorial Conference Actes du Colloque International de Luminy, Springer, 1993, Link
  • Baik, J; Kriecherbauer, T; Li, L-C; McLaughlin, KT-R; Tomei, C (editors), "Integrable Systems and Random Matrices": In Honor of Percy Deift, AMS, 2008. Link
  • Beals, R; Wong, R (authors), "Special Functions and Orthogonal Polynomials", Cambridge University Press, 2016. Link
  • Błaszak, M (author), "Quantum versus Classical Mechanics and Integrability Problems": towards a unification of approaches and tools, Springer, 2019. Link. [You are welcome to contact the author directly about this book here.]
  • Bluman, GW;  Anco, SC (authors), "Symmetry and Integration Methods for Differential Equations", Springer, 2002. Link
  • Bluman, GW; Cheviakov, AF;  Anco, SC (authors), "Applications of Symmetry Methods to Partial Differential Equations", Springer, 2010. Link
  • Bobenko, AI (editor), "Advances in Discrete Differential Geometry", Springer, 2016. Link
  • Bobenko, AI; Suris, YuB (authors), "Discrete Differential Geometry. Integrable Structure", AMS, 2008. Link
  • Bolsinov, A; Morales-Ruiz, JJ; Zung, NT (authors), "Geometry and Dynamics of Integrable Systems", Birkhäuser (available by Springer Nature Link), 2016. Link
  • Buchstaber, VM; Dubrovin, BA; Krichever, IM (editors), "Topology, Geometry, Integrable Systems, and Mathematical Physics": Novikov’s Seminar 2012–2014, AMS, 2014. Link
  • Buchstaber, VM; Konstantinou-Rizos, S; Mikhailov, AV (editors), "Recent Developments in Integrable Systems and Related Topics of Mathematical Physics": Kezenoi-Am, Russia, 2016, Springer, 2018. Link
  • Calogero, F (author), "Classical Many-Body Problems Amenable to Exact Treatments"  (Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space, Springer, 2001, Link
  • Calogero, F (author), "Isochronous Systems", Oxford University Press, 2012. Link
  • Calogero, F (author), "Zeros of Polynomials and Solvable Nonlinear Evolution Equations", Cambridge University Press, 2018. Link
  • Calogero, F; Degasperis, A (authors), "Spectral Transform and Solitons": Tools to Solve and Investigate Nonlinear Evolution Equations, North Holland (imprint), 1982, Link.
  • Carretero-González, R; Frantzeskakis, DJ; Kevrekidis, PG (authors), "Nonlinear Waves & Hamiltonian Systems": From One To Many Degrees of Freedom, From Discrete To Continuum, Oxford University Press, 2024. Link
  • Cherniha, R;  Serov, M; Pliukhin O (authors), "Nonlinear Reaction-Diffusion-Convection Equations": Lie and Conditional Symmetry, Exact Solutions and Their Applications, CRC Press, 2018. Link
  • Choquet-Bruhat, Y (author) and DeWitt-Morette, C (editor), "Analysis, Manifolds and Physics", Part II - Revised and Enlarged Edition, Elsevier, 2000. Link
  • Constantin, A (author), "Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis", CBMS-SIAM, 2010. Link
  • Conte, R; Musette, M (authors), "The Painlevé Handbook", Springer, 2020. Link. [Access to the Appendix is Free]
  • Cushman, RH; Bates, LM (authors), "Global Aspects of Classical Integrable Systems", Birkhäuser (available by Springer Nature Link), 2015. Link
  • De Lucas, J; Sardón Muñoz, C (authors), "A Guide to Lie Systems with Compatible Geometric Structures", World Scientific 2020. Link
  • Debnath, L (editor), "Nonlinear Waves", Cambridge University Press, 2009. Link
  • Deift, P (author), "Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach", AMS, 2000. Link
  • Dickey, LA (author), "Soliton Equations and Hamiltonian Systems" 2nd Edition, World Scientific, 2003. Link
  • Dixon, JM; Tuszynski, JA; Clarkson, PA (authors), "From Nonlinearity to Coherence": Universal Features of Nonlinear Behaviour in Many-body Physics, Oxford University Press, 1997. Link
  • Dorodnitsyn, V (author), "Applications of Lie Groups to Difference Equations", Routledge T&F, 2010. Link
  • Drazin, PG; Johnson, RS (authors), "Solitons": An Introduction, Cambridge University Press, 1989. Link
  • Duistermaat, JJ (author), "Discrete integrable systems: QRT maps and elliptic surfaces", Springer, 2010. Link
  • Dunajski, M (author), "Solitons, Instantons, and Twistors", Second Edition, Oxford University Press, 2024. Link
  • Duval, C; Ovsienko, V; Guieu, L (editors),"The Orbit Method in Geometry and Physics": In Honor of A.A. Kirillov, Brikhäuser (available in Spriger Link), 2003. Link
  • Ebrahimi-Fard, K; Liñán, MB (editors), "Discrete Mechanics, Geometric Integration and Lie–Butcher Series": DMGILBS, Madrid, May 2015, Springer, 2018. Link
  • Elaydi, S; Cashing, J; Lasser, R; Ruffing, A; Papageorgiou, V; van Assche, W (editors), "Difference Equations, Special Functions and Orthogonal Polynomials": Proceedings of the International Conference, Munich, Germany, 25 – 30 July 2005, World Scientific, 2007. Link
  • Etingof, P; Latour, F (authors), "The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems", Oxford University Press, 2005. Link
  • Euler, N (editor), "Nonlinear Systems and Their Remarkable Mathematical Structures", Vol. 1, CRC Press, Taylor & Francis, 2018. Link 
  • Euler, N; Nucci, MC (editors), "Nonlinear Systems and Their Remarkable Mathematical Structures", Vol. 2, CRC Press, Taylor & Francis, 2019. Link
  • Euler, N; Zhang, D (editors), "Nonlinear Systems and Their Remarkable Mathematical Structures", Vol. 3: Contributions from China, CRC Press, Taylor & Francis, 2021. Link
  • Faddeev, L; Van Moerbeke, P; Lambert, F (editors), "Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete": Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete St. Petersburg, Russia, 15-19 September 2002. Springer, 2006. Link
  • Fedorov, Yu; Kozlov, VV (authors), "A Memoir on Integrable Systems", Springer, 2022. Link
  • Fokas, AS (author), "A Unified Approach to Boundary Value Problems", CBMS-SIAM, 2008. Link
  • Fokas, AS (author), "Ways of Comprehending": The Grand Illusion and the Essence of being Human, World Scientific, 2024. Link
  • Fokas, AS; Gelfand, IM (editors), "Algebraic Aspects of Integrable Systems": In Memory of Irene Dorfman, Springer, 1997. Link
  • Fokas, AS; Its, AR; Kapaev, AA (authors), "Painlevé Transcendents: The Riemann-Hilbert Approach", AMS, 2006. Link
  • Fokas, AS; Kaxiras, E (authors), "Modern Mathematical Methods for Scientists and Engineers": A Street-Smart Introduction, World Scientific, 2023. Link
  • Fushchich, WI; Shtelen, WM;  Serov, NI (authors), "Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics", Springer, 1993, Link
  • Gaeta, G (author), "Nonlinear Symmetries and Nonlinear Equations", Springer, 1994. Link
  • Gaeta, G (editor), "Perturbation Theory":Mathematics, Methods and Applications, Springer, 2022. Link
  • Gaeta, G; Rodriguez, MA (authors), "Lectures on Hyperhamiltonian Dynamics and Physical Applications", Springer, 2017. Link
  • Galaktionov, VA; Svirshchevskii, SR (authors), "Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics", Taylor & Francis, 2007. Link
  • Galiev, SU (author), "Evolution of Extreme Waves and Resonances" Volume I, Taylor & Francis, 2020. Link
  • Galiev, SU (author), "Extreme Waves and Shock-Excited Processes in Structures and Space Objects" Volume II, Taylor & Francis, 2020. Link
  • Gesztesy, F; Holden, H; Michor, J; Teschl, G (authors), "Soliton Equations and Their Algebro-Geometric Solutions", Cambridge University Press, 2008. Link
  • Gohberg, I; Manojlovic, N; Santos, AF (editors), "Factorization and Integrable Systems": Summer School in Faro, Portugal, September 2000, Springer, 2003. Link
  • Grammaticos, B; Tamizhmani, T; Kosmann-Schwarzbach, Y (editors), "Discrete Integrable Systems", Springer, 2004. Link
  • Gu, C; Hu, H; Zhou, Z (authors), "Darboux Transformations in Integrable Systems": Theory and their Applications to Geometry, Springer, 2005. Link
  • Guest, MA (author), "Harmonic Maps, Loop Groups, and Integrable Systems", Cambridge University Press, 1997. Link
  • Guest, MA (author), "From Quantum Cohomology to Integrable Systems", Oxford University Press, 2008, Link
  • Guest, MA; Hertling, C (authors), "Painlevé III: A Case Study in the Geometry of Meromorphic Connections", Springer, 2017. Link
  • Guest, MA; Miyaoka, R; Ohnita, Y (editors), "Differential Geometry and Integrable Systems", AMS, 2002. Link
  • Guest, MA; Miyaoka, R; Ohnita, Y (editors), "Integrable Systems, Topology, and Physics", AMS, 2002. Link
  • Harnad, J; Balogh, F (authors), "Tau Functions and their Applications", Cambridge University Press, 2021. Link
  • Harnad, J; Sabidussi, G; Winternitz, P (editors), "Integrable Systems: From Classical to Quantum", AMS, 2000. Link 
  • Henry, D (editor), "Nonlinear Dispersive Waves": Based on the 2023 Workshop at University College Cork, Ireland. Birkhäuser (available by Springer Nature), 2024. Link
  • Hietarinta, J; Joshi N; Nijhoff, FW (authors), "Discrete Systems and Integrability", Cambridge University Press, 2016. Link
  • Hirota, R (author), Edited and Translated by Atsushi Nagai, Jon Nimmo and Claire Gilson, "The Direct Method in Soliton Theory", Cambridge University Press, 2004. Link
  • Hitchin, NJ; Segal, GB; Ward, RS (authors), "Integrable Systems": Twistors, Loop Groups, and Riemann Surfaces, Oxford Univetsity Press, 1999. Link
  • Hoffmann, T; Kilian, M; Leschke, K; Martin, F (editors), "Minimal Surfaces: Integrable Systems and Visualisation": m:iv Workshops, 2016–19. Springer, 2021. Link
  • Holm, DD (author), "Geometric Mechanics, Part I": Dynamics and Symmetry , 2nd edition, World Scientific, 2011. Link
  • Holm, DD (author), "Geometric Mechanics, Part II": Rotating, Translating and Rolling, 2nd edition, World Scientific, 2011. Link
  • Holm, DD; Schmah, T; Stoica, C (authors), "Geometric Mechanics and Symmetry": From Finite to Infinite Dimensions, Oxford University Press, 2009. Link
  • Hoppe, J (author), "Lectures on Integrable Systems", Springer, 1992. Link
  • Hydon, PE (author), "Symmetry Methods for Differential Equations": A Beginner's Guide, Cambridge University Press, 2000. Link
  • Hydon, PE (author), "Difference Equations by Differential Equation Methods", Cambridge University Press, 2014. Link
  • Ibragimov, NH (editor), "CRC Handbook of Lie Group Analysis of Differential Equations", Volume I: Symmetries, Exact Solutions, and Conservation Laws, Routledge T&F, 1993. Link
  • Ibragimov, NH (editor), "CRC Handbook of Lie Group Analysis of Differential Equations", Volume II: Applications in Engineering and Physics Sciences, Routledge T&F, 1995. [A link to the publisher is not available].
  • Ibragimov, NH (editor), "CRC Handbook of Lie Group Analysis of Differential Equations", Volume III: New Trends in Theoretical Developments and Computational Methods, Routledge T&F, 1995. Link
  • Infeld, E; Rowlands, G (authors), "Nonlinear Waves, Solitons and Chaos", Cambridge University Press, 2000. Link
  • Iohara, K; Morier-Genoud, S; Remy, B (editors), "Symmetries, Integrable Systems and Representations", Springer, 2013. Link
  • Jimbo, M (editor), "Yang-Baxter Equation in Integrable Systems", World Scientific, 1990. Link
  • Johnson, RS (author), "A Modern Introduction to the Mathematical Theory of Water Waves", Cambridge University Press, 1997. Link
  • Joshi, N (author), "Discrete Painlevé Equations", AMS, 2019. Link
  • Kac, VG; Cheung, P (authors), "Quantum Calculus", Springer, 2002. Link
  • Kac, VG; Olver, PJ; Winternitz, P; Özer, T (Editors), "Symmetries, Differential Equations and Applications": SDEA-III, İstanbul, Turkey, August 2017, Springer, 2018. Link
  • Kac, VG; Raina, AK; Rozhkovskaya, N (authors), "Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras" 2nd Edition, World Scientific, 2013. Link
  • Kalnins, EG; Kress, JM; Miller Jr, W (authors), "Separation of Variables and Superintegrability": The symmetry of solvable systems, IOPscience, 2018. Link
  • Kamke, E (author), "Differentialgleichungen Lösungsmethoden und Lösungen", Springer, 1977 (reprinted from the original). Link. See also "Differentialgleichungen Lösungsmethoden Und Lösungen Band I", Chelsea Publishing Company, 1948. Link [Internet Archive, free access]    
  • Kamke, E (author), "Differentialgleichungen Lösungsmethoden und Lösungen II": Partielle Differentialgleichungen Erster Ordnung für eine Gesuchte Funktion, Springer, 1979 (reprinted from the original). Link
  • Kasman, A (author), "Glimpses of Soliton Theory: The Algebra and Geometry of Nonlinear PDEs" 2nd edition, AMS, 2023. Link
  • Kato, T (author), "Dynamical Scale Transform in Tropical Geometry", World Scientific, 2016. Link
  • Klein, C; Saut, J-C (authors), "Nonlinear Dispersive Equations":Inverse Scattering and PDE Methods, Springer, 2021. Link
  • Kodama, Y (author), "KP Solitons and the Grassmannians": Combinatorics and Geometry of Two-Dimensional Wave Patterns, Springer, 2017. Link
  • Kodama, Y (author), "Solitons in Two-Dimensional Shallow Water", SIAM, 2018. Link
  • Konopelchenko, BG (author), "Nonlinear Integrable Equations": Recursion Operators, Group-Theoretical and Hamiltonian Structures of Soliton Equations, Springer, 1987. Link
  • Konopelchenko, BG (author), "Introduction to Multidimensional Integrable Equations": The Inverse Spectral Transform in 2+1 Dimensions, Plenum Monographs in Nonlinear Physics (available in Springer Link), 1992. Link
  • Konopelchenko, BG (author), "Solitons in Multidimensions": Inverse Spectral Transform Method, World Scientific, 1993, Link
  • Kosmann-Schwarzbach, Y (author), "Groups and Symmetries": From Finite Groups to Lie Groups, Springer, 2022. Link
  • Kosmann-Schwarzbach, Y; Schwarzbach, BE (authors), "The Noether Theorems":  Invariance and Conservation Laws in the Twentieth Century, Springer, 2011. Link
  • Kosmann-Schwarzbach, Y; Tamizhmani, KM; Grammaticos, B (editors), "Integrability of Nonlinear Systems", Springer, 2004. Link
  • Krasil'shchik, J; Verbovetsky, A; Vitolo, R (authors), "The Symbolic Computation of Integrability Structures for Partial Differential Equations", Springer, 2017. Link
  • Kundu, A (editor), "Classical and Quantum Nonlinear Integrable Systems": Theory and Application, Taylor & Francis, 2003. Link
  • Kuo, S (author), "Nonlinear Waves and Inverse Scattering Transform", World Scientific, 2023. Link
  • Kupershmidt, BA (author), "Elements of Superintegrable Systems": Basic Techniques and Results, D. Reidel Publishing Company (available by Springer Nature Link), 1987. Link
  • Kupershmidt, BA (editor), "Integrable and Superintegrable Systems", World Scientific, 1990. Link
  • Lakshmanan, M; Rajasekar, S (authors), "Nonlinear Dynamics": Integrability, Chaos and Patterns, Springer, 2003. Link
  • Laurent-Gengoux, C; Pichereau, A; Vanhaecke, P (authors), "Poisson Structures", Springer, 2013. Link
  • Levi, D; Olver, PJ; Thomova, Z; Winternitz, P (editors), "Symmetries and Integrability of Difference Equations", Cambridge University Press, 2011. Link
  • Levi, D; Rebelo, R; Winternitz, P (editors), "Symmetries and Integrability of Difference Equations": Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016, Springer, 2017. Link
  • Levi, D; Vinet, L; Winternitz, P (editors), "Symmetries and Integrability of Difference Equations", AMS, 1996. Link
  • Levi, D; Winternitz, P; Yamilov, RI (authors), "Continuous Symmetries and Integrability of Discrete Equations", AMS, 2022. Link
  • Llibre, J; Ramírez, R (authors), "Inverse Problems in Ordinary Differential Equations and Applications", Birkhäuser (available in Springer Link), 2016. Link
  • MacKenzie, R; Paranjape, MB; Zakrzewski, WJ (editors), "Solitons": Properties, Dynamics, Interactions, Applications, Springer, 2000. Link
  • Maclagan, D; Sturmfels, B (authors), "Introduction to Tropical Geometry", AMS, 2015. Link
  • Manin, YuI (author) translated from Russian and edited by Leites, D. "Introduction to the Theory of Schemes", Springer, 2018. Link
  • Manton, N; Sutcliffe, P (authors), "Topological Solitons", Cambridge University Press, 2004. Link
  • Meleshko, SV (author), "Methods for Constructing Exact Solutions of Partial Differential Equations": Mathematical and Analytical Techniques with Applications to Engineering, Springer, 2005. Link
  • Mikhailov, AV (editor), "Integrability", Springer, 2009. Link
  • Miwa, T; Jimbo, M; Date, E (authors) translated by Reid, M. "Solitons": Differential Equations, Symmetries and Infinite Dimensional Algebras, Cambridge University Press, 1999. Link
  • Newell, AC (author), "Solitons in Mathematics and Physics", SIAM, 1985. Link
  • Nijhoff, FW; Shi, Y; Zhang, D (editors), "Asymptotic, Algebraic and Geometric Aspects of Integrable Systems": In Honor of Nalini Joshi On Her 60th Birthday, TSIMF,  Sanya, China, April 9–13, 2018, Springer, 2018. Link
  • Novikov, S; Krichever, I; Ogievetsky, O; Shlosman, S (editors), "Integrability, Quantization, and Geometry: I": Integrable Systems, AMS, 2021. Link
  • Novikov, S; Krichever, I; Ogievetsky, O; Shlosman, S (editors), "Integrability, Quantization, and Geometry: II": Quantum Theories and Algebraic Geometry, AMS, 2021. Link
  • Olver, PJ (author), "Applications of Lie Groups to Differential Equations", Springer, 1993. Link
  • Olver, PJ (author), "Equivalence, Invariants and Symmetry", Cambridge University Press, 1995. Link
  • Olver, PJ (author), "Classical Invariant Theory", Cambridge University Press, 1999. Link
  • Osborne, A (author), "Nonlinear Ocean Waves and the Inverse Scattering Transform", Elsevier, 2010. Link
  • Ovsienko, V;  Tabachnikov, S (authors), "Projective Differential Geometry Old and New": From the Schwarzian Derivative to the Cohomology of Diffeomorphism Groups, Cambridge University Press, 2004. Link
  • Petrera, M (author), "Mathematical Physics III - Integrable Systems of Classical Mechanics", Lagos Verlag Berlin, 2015. Link [See also the following books by the same author: "Mathematical Physics I", Link, and "Mathematical Physcs II", Link]
  • Polyanin, AD (author), "Handbook of Exact Solutions to Mathematical Equations", Chapman and Hall/CRC, 2025. Link
  • Polyanin, AD;  Sorokin, VG; Zhurov, AI (authors), "Delay Ordinary and Partial Differential Equations", Taylor & Francis, 2024. Link
  • Polyanin, AD; Zaitsev, VF (authors),"Handbook of Nonlinear Partial Differential Equations", Taylor & Francis, 2012. Link
  • Polyanin, AD; Zaitsev, VF (authors), "Handbook of Ordinary Differential Equations": Exact Solutions, Methods, and Problems , Taylor & Francis, 2017. Link
  • Polyanin, AD; Zhurov, A (authors), "Separation of Variables and Exact Solutions to Nonlinear PDEs", Taylor & Francis, 2022. Link
  • Prasolov, VV (author), "Problems and Theorems in Linear Algebra", AMS, 1994. Link
  • Prasolov, VV (author), "Polynomials", Springer, 2004. Link
  • Rogers, C (author), "A Nonlinear Progress to Modern Soliton Theory", Cambridge Scholars Publishing, 2022. Link
  • Rogers, C; Schief, WK (authors), "Bäcklund and Darboux Transformations": Geometry and Modern Applications in Soliton Theory, Cambridge University Press, 2002. Link [Note: This book has been transcribed into Chinese by Z.X. Zhou. Link]
  • Šamaj, L; Bajnok, Z (authors), "Introduction to the Statistical Physics of Integrable Many-body Systems", Cambridge University Press, 2013. Link
  • Schöbel, K (author), "An Algebraic Geometric Approach to Separation of Variables", Springer, 2015. Link
  • Semenoff, G; Vinet, L (editors), "Particles and Fields", Springer, 1999. Link
  • Shabat, AB; González-López, A; Mañas, M; Martínez Alonso, L; Rodríguez, MA (editors), "New Trends in Integrability and Partial Solvability", Springer, 2004. Link
  • Sokolov, V (author), "Algebraic Structures in Integrability"  Foreword by Victor Kac, World Scientific, 2020. Link
  • Suris, YuB  (author), "The Problem of Integrable Discretization": Hamiltonian Approach, Birkhäuser (available in Springer Link), 2003. Link
  • Sutherland, B (author), "Beautiful Models": 70 Years of Exactly Solved Quantum Many-Body Problems, World Scientific, 2004. Link
  • Terng, C-L (editor), "Integrable Systems, Geometry, and Topology", AMS, 2006. Link
  • Vanhaecke, P (author), "Integrable Systems in the realm of Algebraic Geometry", Springer, 1996. Link
  • Vu, PL (author), "Inverse Scattering Problems and Their Application to Nonlinear Integrable Equations" 2nd edition, Taylor & Francis, 2023. Link
  • Weinberg, EJ (author), "Classical Solutions in Quantum Field Theory": Solitons and Instantons in High Energy Physics. Cambridge University Press, 2012. Link
  • Yang, B; Yang, J (authors); "Rogue Waves in Integrable Systems", Springer, 2024. Link
  • Yang, J (author), "Nonlinear Waves in Integrable and Nonintegrable Systems", SIAM, 2010. Link
  • Zakharov, VE (editor), "What Is Integrability?", Springer. 1991. Link
  • Zwillinger, D; Dobrushkin, V (authors), "Handbook of Differential Equations" 4th edition, Taylor & Francis, 2021. Link


A List of Some Prominent Mathematical Physicists:

  • Abel, Niels Henrik: The Wikipedia Link
  • d'Alembert, Jean le Rond: The Wikipedia Link
  • Arnold, Vladimir: The Wikipedia Link
  • Banach, Stefan: The Wikipedia Link
  • Bäcklund, Albert Victor: The Wikipedia Link
  • Baxter, Rodney: The Wikipedia Link
  • Bernoulli, Daniel: The Wikipedia Link
  • Bernoulli, Jacob; The Wikipedia Link
  • Birkhoff, George David: The Wikipedia Link
  • Bogolyubov, Nikolay: The Wikipedia Link
  • Bullough, Robin K: The Wikipedia Link
  • Calogero, Francesco: The Wikipedia Link. See also the Google Scholar Link
  • Cantor, Georg: The Wikipedia Link
  • Cartan, Elie: The Wikipedia Link. See also, Cartan, Elie  (author), "Leçons sur les invariants intégraux", Paris A. Hermann, 1922. Link [Internet Archive, free access]
  • Cauchy, Augustin-Louis: The Wikipedia Link
  • Darboux, Jean Gaston: The Wikipedia Link. See also Darboux, Gaston (author), "Leçons sur les systèmes orthogonaux et les coordonnées curvilignes", Paris Gauthier-Villars, 1910. Link [Internet Archive, free access]
  • De Vries, Gustav: The Wikipedia Link
  • Dirac, Paul: The Wikipedia Link
  • Dirichlet, Peter Gustav Lejeune: The Wikipedia Link
  • Drinfeld, Vladimir: The Wikipedia Link
  • Einstein, Albert: The Wikipedia Link
  • Euler, Leonhard: The Wikipedia Link to"Wissenschaftliches Werk Leonhard Eulers" [See also the English Wikipedia Link]
  • Fokas, Athanassios S: The Wikipedia Link. See also The Academy of Europe Link 
  • Fourier, Joseph: The Wikipedia Link
  • Fushchych, Wilhelm I: The Kiev Institute of Mathematics Link
  • Gauß, Friedrich Carl: The Wikipedia Link and the Wikisource Link 
  • Galilei, Galileo: The Wikipedia Link
  • Gelfand, Isreal: The Wikipedia Link
  • Gödel, Kurt: The Wikipedia Link
  • Green, George: The Wikipedia Link
  • Hamilton, William Rowan: The Wikipedia Link
  • Hawking, Stephen: The Wikipedia Link
  • Heaviside, Oliver: The Wikipedia Link
  • Heisenberg, Werner: The Wikipedia Link
  • Hilbert, David: The Wikipedia Link
  • Its, Alexander: The Wikipedia Link
  • Jacobi, Carl Gustav Jacob: The Wikipedia Link.  See also Jacobi, Carl Gustav Jacob (author), "C. G. J. Jacobi’s Collected Works" (consists of eight volumes, 4012 pages), AMS, 1969. Link. See also the book by L Koenigsberger (author), "Carl Gustav Jacob Jacobi": Festschrift zur Feier der Hundertsten Wiederkehr Seines Geburtstages, B. G. Teubner, 1904. Link [Internet Archive, free access]
  • Kac, Victor: The Wikipedia Link
  • Kadomtsev, Boris: The Wikipedia Link
  • Keller, Joseph Bishop: The Wikipedia Link
  • Kepler, Johannes: The Wikipedia Link
  • Kolmogorov, Andrey: The Wikipedia Link
  • Korteweg, Diederik: The Wikipedia Link.  See also the article Korteweg, DJ and De Vries, G, "On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves", Philosophical Magazine, 39 (240) (1895) 422–443, doi.org/10.1080/14786449508620739. Link
  • Kovalevskaya, Sofya: The Wikipedia Link. See also  Kowalevski, Sophie (author), "Sur le probleme de la rotation d'un corps solide autour d'un point fixe",  Acta Math. 12 177 - 232, 1889, doi.org/10.1007/BF02592182. Link [Project Euclid, open access]
  • Krichever, Igor: The Wikipedia Link
  • Kruskal, Martin David: The Wikipedia Link
  • Kupershmidt, Boris A: The ResearchGate Link
  • Lagrange, Joseph-Louis: The Wikipedia Link
  • Landau, Edmund: The Wikipedia Link
  • Laplace, Pierre-Simon: The Wikipedia Link
  • Lax, Peter: The Wikipedia Link
  • Leibniz, Gottfried Wilhelm:   "Leibniz - Edition: Die Akademie-Ausgabe, Collected papers of Gottfried Wilhelm Leibniz". Leibniz-Archiv/Leibniz-Forschungsstelle Hannover, Link 
  • Lie, Sophus: The Wikipedia Link. See also the Collected Works of Sophus Lie, Based on a grant from the Norwegian Research Fund of 1919 with the support of the Videnskapsakademi in Oslo and the Academy of Sciences in Leipzig. Leipzig : B. G. Teubner, 1922-1960.  Link [Internet Archive, free access]
  • Lighthill, Michael James: The Wikipedia Link
  • Liouville, Joseph: The Wikipedia Link
  • Lorentz, Hendrik: The Wikipedia Link
  • Lyapunov, Aleksandr: The Wikipedia Link
  • Mandelbrot, Benoit: The Wikipedia Link
  • Maxwell. James Clerk: The Wikipedia Link
  • Minkowski, Hermann: The Wikipedia Link
  • Miura, Robert M: The Wikipedia Link
  • Moser, Jürgen: The Wikipedia Link
  • Neumann, Carl: The Wikipedia Link
  • Newton, Isaac: The Wikipedia Link
  • Noether, Emmy: The Wikipedia Link. See also the book by Y Kosmann-Schwarzbach (author); translated by BE Schwarzbach, "The Noether Theorems": Invariance and Conservation Laws in the Twentieth Century, Springer, 2011. Link
  • Novikov, Sergei: The Wikipedia Link
  • Painlevé, Paul: The Wikipedia Link. See also  Painlevé, Paul (author), "Lectures on the Analytical Theory of Differential Equations", given in Stockholm (September, October, November 1895) at the invitation of His Majesty the King of Sweden and Norway, Paris A. Hermann, 1897. Link  [Internet Archive, free access] 
  • Pauli, Wolfgang: The Wikipedia Link
  • Penrose, Roger: The Wikipedia Link
  • Petviashvili, Vladimir: The Wikipedia Link
  • Picard, Emile: The Wikipedia Link
  • Planck, Max: The Wikipedia Link
  • Poincaré, Henri: The Wikipedia Link
  • Poisson, Siméon Denis: The Wikipedia Link
  • Riemann, Bernhard: The Wikipedia Link
  • Russell, John Scott: The Wikipedia Link
  • Schrödinger, Erwin: The Wikipedia Link
  • Shabat, AB: The Google Scholar Link
  • Sommerfeld, Arnold: The Wikipedia Link
  • Stokes, George: The Wikipedia Link
  • Von Helmholtz, Hermann: The Wikipedia Link
  • Weierstrass, Karl Theodor Wilhelm: The Wikipedia Link
  • Weyl, Hermann: The Wikipedia Link
  • Whitham, Gerald Beresford: The Wikipedia Link
  • Wigner, Eugene: The Wikipedia Link
  • Yang, Chen-Ning: The Wikipedia Link
  • Zabusky, Norman: The Wikipedia Link
  • Zakharov, Vladimir E: The Wikipedia Link


Other Useful Links:

  • Digital Library of Mathematical Functions, NIST (U.S. Department of Commerce), 2010-2024. Link [free access]
  • Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen (Erschien 1898–1935, Neubearbeitung 1939–1967), Wikisource.  Link [free access]
  • EqWorld: The World of Mathematical Equations. Link [free access]
  • OEIS Wiki: The On-Line Encyclopedia of Integer Sequences® (OEIS®) Wiki. Link


Book Reviews: Those will be posted here.

Send in your Book Reviews or Recommendations: You are very welcome to publish your Book Reviews in the subject of Nonlinear Mathematical Physics on this page and to suggest books for the above list of Literature Recommendations . To do so, please send your material to the following email address.