Veselov-Novikov equation as a natural two-dimensional generalization of the Korteweg-de Vries equation. (English. Russian original) Zbl 0639.35072
Theor. Math. Phys. 70, 219-223 (1987); translation from Teor. Mat. Fiz. 70, No. 2, 309-314 (1987).
Summary: The Miura transformation between KdV and MKdV solutions is generalized to the two-dimensional case. An integrable equation associated with the two- dimensional Dirac operator - the modified Veselov-Novikov equation - is introduced.
MSC:
| 35Q99 | Partial differential equations of mathematical physics and other areas of application |
| 35A30 | Geometric theory, characteristics, transformations in context of PDEs |
References:
| [1] | A. P. Veselov and S. P. Novikov, Dokl. Akad. Nauk SSSR,279, 784 (1984). |
| [2] | S. V. Manakov, Usp. Mat. Nauk,31(5), 245 (1976). |
| [3] | P. G. Grinevich and S. V. Manakov, Funktsional. Analiz i Ego Prilozhen.,20, 14 (1985). |
| [4] | V. E. Zakharov and S. V. Manakov, Funktsional. Analiz i Ego Prilozhen.,19, 11 (1985). |
| [5] | V. E. Zakharov and A. B. Shabat, Funktsional. Analiz i Ego Prilozhen.,8, 43 (1974). |
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