International Society of Nonlinear Mathematical Physics

Book Reviews and Recommendations

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; Novikov, SP (editors), "Dynamical Systems IV": Symplectic Geometry and its Applications"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
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; Degasperis, A (authors), "Spectral Transform and Solitons": Tools to Solve and Investigate Nonlinear Evolution Equations, North Holland (imprint), 1982, 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 (availaböle 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
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
Dorodnitsyn, V (author), "Applications of Lie Groups to Difference Equations", Routledge T&F, 2010. 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
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
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, 20224. 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, 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 could not be found].
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
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
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
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
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; 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
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
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
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
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 I: Dynamical Systems and Classical Mechanics", Lagos Verlag Berlin, 2014. Link
Petrera, M (author), "Mathematical Physics II: Classical Statistical Mechanics", Lagos Verlag Berlin, 2014. Link
Petrera, M (author), "Mathematical Physics III - Integrable Systems of Classical Mechanics", Lagos Verlag Berlin, 2015. 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]
Schöbel, K (author), "An Algebraic Geometric Approach to Separation of Variables", Springer, 2015. 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
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
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
Zakharov, VE (editor), "What Is Integrability?", Springer. 1991. Link

Some Classical and Historically Important Literature:

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]
Cartan, Elie (author), "Leçons sur les invariants intégraux", Paris A. Hermann, 1922. Link [Internet Archive, free access]
Darboux, Gaston (author), "Leçons sur les systèmes orthogonaux et les coordonnées curvilignes", Paris Gauthier-Villars, 1910. Link [Internet Archive, free access]
Jacobi, Carl Gustav Jacob (author), "C. G. J. Jacobi’s Collected Works" (consists of eight volumes, 4012 pages), AMS, 1969. Link
Kamke, E (author), "Differentialgleichungen Lösungsmethoden Und Lösungen Band I", Chelsea Publishing Company, 1948. Link [Internet Archive, free access]
Koenigsberger, L (author), "Carl Gustav Jacob Jacobi": Festschrift zur Feier der Hundertsten Wiederkehr Seines Geburtstages, B. G. Teubner, 1904. Link [Internet Archive, free access]
Kosmann-Schwarzbach, Y (author); translated by Schwarzbach, BE, "The Noether Theorems": Invariance and Conservation Laws in the Twentieth Century, Springer, 2011. Link
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
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]
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]

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]
Carl Friedrich Gauß. A collection of references. Wikisource. Link [free access]
Leibniz - Edition: Die Akademie-Ausgabe, Collected papers of Gottfried Wilhelm Leibniz. Leibniz-Archiv/Leibniz-Forschungsstelle Hannover, Link [free access]

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 .