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Soliton equations and Hamiltonian systems. 2nd ed. (English) Zbl 1140.35012
Advanced Series in Mathematical Physics 26. Singapore: World Scientific (ISBN 981-238-173-2/hbk). xi, 408 p. (2003).
Publisher’s description: The theory of soliton equations and integrable systems has developed rapidly during the last 20 years with numerous applications in mechanics and physics. For a long time books in this field have not been written but the flood of papers was overwhelming: many hundreds, maybe thousands of them. All this followed one single work by Gardner, Green, Kruskal, and Mizura about the Korteweg-de Vries equation (KdV) which, had seemed to be merely an unassuming equation of mathematical physics describing waves in shallow water.
This branch of science is attractive because it is one of those which revives the interest in the basic principles of mathematics, a beautiful formula.
See the review of the first edition in Zbl 0753.35075.

35Q51 Soliton equations
35-02 Research exposition (monographs, survey articles) pertaining to partial differential equations
37-03 History of dynamical systems and ergodic theory
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
35Q53 KdV equations (Korteweg-de Vries equations)
35Q58 Other completely integrable PDE (MSC2000)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)