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Variational principles for some nonlinear partial differential equations with variable coefficients. (English) Zbl 1135.35303
The author suggests a method to search for various variational principles for physical problems. The most interesting features of the proposed method, compared with Noether’s theorem, are its extreme simplicity and concise results for a wide range of nonlinear problems.

MSC:
35A15 Variational methods applied to PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
35Q55 NLS equations (nonlinear Schrödinger equations)
37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
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