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Variational principle for equations integrable by the inverse problem method. (English. Russian original) Zbl 0473.35075

Funct. Anal. Appl. 14, 43-44 (1980); translation from Funkts. Anal. Prilozh. 14, No. 1, 55-56 (1980).

MSC:

35R30 Inverse problems for PDEs
35A15 Variational methods applied to PDEs
Full Text: DOI

References:

[1] D. Y. Benney, ”Some properties of long nonlinear waves,” Stud. Appl. Math.,52, No. 1, 45-50 (1973). · Zbl 0259.35011
[2] R. M. Miura, ”Conservation laws for the fully nonlinear long wave equations,” Stud. Appl. Math.,53, No. 1, 45-56 (1974). · Zbl 0306.76020
[3] B. A. Kupershmit and Yu. I. Manin, ”Equation of long waves with free surface. I. Conservation laws and solutions; II. Hamiltonian structure and higher equations,” Funkts. Anal.,11, No. 3, 31-42 (1977);12, No. 1, 25-37 (1978).
[4] S. V. Manakov, ”On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Zh. Eksp. Teor. Fiz.,65, No. 2, 505-516 (1973).
[5] V. E. Zakharov, ”Hamiltonian formalism for waves in nonlinear media with dispersion,” Izv. Vyssh. Uchebn. Zaved., Radiofiz.,22, No. 4, 431-453 (1974).
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