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, Mark J (author), "Nonlinear Dispersive Waves": Asymptotic Analysis and Solitons, Cambridge University Press, 2011. Link
  • Ablowitz, MJ; Prinari, B; Trubatch, AD (authors), "Discrete and Continuous Nonlinear Schrödinger Systems", Cambridge University Press, 2003. Link
  • Błaszak, Maciej (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, George W;  Anco, Stephen C (authors), "Symmetry and Integration Methods for Differential Equations", Springer, 2002. Link
  • Bluman, George W ; Cheviakov, Alexei F;  Anco, Stephen C (authors), "Applications of Symmetry Methods to Partial Differential Equations", Springer, 2010. Link
  • Bobenko, Alexander I; Suris, Yuri B (authors), "Discrete Differential Geometry. Integrable Structure", AMS, 2008. Link
  • Calogero, Francesco (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, Francesco (author), "Isochronous Systems", Oxford University Press, 2012. Link
  • Calogero, Francesco; Degasperis, Antonio (authors), "Spectral Transform and Solitons": Tools to Solve and Investigate Nonlinear Evolution Equations, North Holland (imprint), 1982, Link.
  • Constantin, Adrian (author), "Nonlinear Water Waves with Applications to Wave-Current Interactions and Tsunamis", CBMS-SIAM, 2010. Link
  • Conte, Robert; Musette, Micheline (authors), "The Painlevé Handbook", Springer, 2020. Link. Access to the Appendix is Free
  • Dorodnitsyn, Vladimir (author), "Applications of Lie Groups to Difference Equations", Routledge T&F, 2010. Link
  • Dunajski, Maciej (author), "Solitons, Instantons, and Twistors" (Second Edition), Oxford University Press, 2024. Link
  • Duval, Christian; Ovsienko, Valentin; Guieu, Laurent (editors),"The Orbit Method in Geometry and Physics":
    In Honor of A.A. Kirillov, Brikhäuser (available in Spriger Link), 2003. Link
  • Euler, Norbert (editor), "Nonlinear Systems and Their Remarkable Mathematical Structures", Vol. 1, Taylor & Francis, 2018. Link 
  • Euler, Norbert; Nucci, Maria Clara (editors), "Nonlinear Systems and Their Remarkable Mathematical Structures", Vol. 2, Taylor & Francis, 2019. Link
  • Euler, Norbert; Zhang, Da-jun (editors), "Nonlinear Systems and Their Remarkable Mathematical Structures", Vol. 3: Contributions from China, Taylor & Francis, 2021. Link
  • Fokas, Athanassios S (author), "A Unified Approach to Boundary Value Problems", CBMS-SIAM, 2008. Link
  • Fokas, Athanassios S (author), "Ways of Comprehending": The Grand Illusion and the Essence of being Human, World Scientific, 2024. Link
  • Fokas, Athanassios S; Its, Alexander R; Kapaev, Andrei A (authors), "Painlevé Transcendents: The Riemann-Hilbert Approach", AMS, 2006. Link
  • Fokas, Athanassios S; Kaxiras, Efthimios (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, Giuseppe (author), "Nonlinear Symmetries and Nonlinear Equations", Springer, 1994. Link
  • Gaeta, Giuseppe (editor), "Perturbation Theory", Springer, 2022. Link
  • Gaeta, Giuseppe; Rodriguez, Miguel A (authors), "Lectures on Hyperhamiltonian Dynamics and Physical Applications", Springer, 2017. Link
  • Grammaticos, Basil; Tamizhmani, Thamizharasi; Kosmann-Schwarzbach, Yvette (editors), "Discrete Integrable Systems", Springer, 20224. Link
  • Hietarinta, J; Joshi N; Nijhoff, FW (authors), "Discrete Systems and Integrability", Cambridge University Press, 2016. Link
  • Holm, Darryl D (author), "Geometric Mechanics, Part I: Dynamics and Symmetry (2nd edition), World Scientific, 2011. Link
  • Holm, Darryl D (author), "Geometric Mechanics, Part II: Rotating, Translating and Rolling (2nd edition), World Scientific, 2011. Link
  • Holm, Darryl D; Schmah, Tanya; Stoica, Cristina (authors), "Geometric Mechanics and Symmetry":
    From Finite to Infinite Dimensions, Oxford University Press, 2009. Link
  • Hydon, Peter E (author), "Symmetry Methods for Differential Equations": A Beginner's Guide, Cambridge University Press, 2000. Link
  • Hydon, Peter E (author), "Difference Equations by Differential Equation Methods", Cambridge University Press, 2014. 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, Yvette; Tamizhmani, KM; Grammaticos, Basil (editors), "Integrability of Nonlinear Systems", Springer, 2004. Link
  • Levi, Decio; Winternitz, Pavel; Yamilov, Ravil I (authors), "Continuous Symmetries and Integrability of Discrete Equations", AMS, 2022. Link
  • Llibre, Jaume; Ramírez, Rafael (authors), "Inverse Problems in Ordinary Differential Equations and Applications", Birkhäuser (available in Springer Link), 2016. Link
  • Manin, Yuri I (author) translated from Russian and edited by Dimitry Leites. "Introduction to the Theory of Schemes", Springer, 2018. Link
  • Nijhoff, Frank W; Shi, Yang; Zhang, Da-jun (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
  • Olver, Peter J (author), "Applications of Lie Groups to Differential Equations", Springer, 1993. Link
  • Olver, Peter J (author), "Equivalence, Invariants and Symmetry", Cambridge University Press, 1995. Link
  • Olver, Peter J (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
  • Prasolov, VV (author), "Problems and Theorems in Linear Algebra", AMS, 1994. Link
  • Prasolov, VV (author), "Polynomials", Springer, 2004. Link
  • Rogers, Colin (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]
  • Sokolov, Vladimir (author), "Algebraic Structures in Integrability"  Foreword by Victor Kac, World Scientific, 2020. Link
  • Suris, Yuri B  (author), "The Problem of Integrable Discretization": Hamiltonian Approach, Birkhäuser (available in Springer Link), 2003. Link
  • Zakharov, Vladimir E (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 (free access on the Internet Archive, in German)
  • Jacobi, Carl Gustav Jacob (author), "C. G. J. Jacobi’s Collected Works" (consists of eight volumes, 4012 pages), AMS, 1969. Link
  • Koenigsberger, Leo (author), "Carl Gustav Jacob Jacobi": Festschrift zur Feier der Hundertsten Wiederkehr Seines Geburtstages, B. G. Teubner, 1904. Link (free access Internet Archive, in German)
  • Kosmann-Schwarzbach, Yvette (author); translated by Schwarzbach, Bertram E, "The Noether Theorems":
    Invariance and Conservation Laws in the Twentieth Century, Springer, 2011. 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 (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 (free access on the Internet Archive, in French)


Other Useful Links:

  • Digital Library of Mathematical Functions, NIST (U.S. Department of Commerce), 2010-2024. Link
  • The Euler Archive: A digital library dedicated to the work and life of Leonhard Euler. Created by Dominic Klyve (Central Washington University) and Lee Stemkoski (Adelphi University). Managed by Erik Tou (University of Washington, Tacoma) and Chris Goff (University of the Pacific). Link (free downloads)
  • Carl Friedrich Gauß. A collection of references. Wikisource. Link
  • 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.

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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.