Geodesic
On equations generated by an operator relation
Sbornik. Mathematics, Tome 36 (1980) no. 3, pp. 351-363 
V. K. Mel'nikov. On equations generated by an operator relation. Sbornik. Mathematics, Tome 36 (1980) no. 3, pp. 351-363. http://geodesic.mathdoc.fr/item/SM_1980_36_3_a4/
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     title = {On equations generated by an operator relation},
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     url = {http://geodesic.mathdoc.fr/item/SM_1980_36_3_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A system of equations generated by an operator relation analogous to the Lax operator representation of the Korteweg–de Vries equation is considered. It is shown that the system of equations obtained in this way possesses several infinite series of conservation laws. Conditions for the existence and uniqueness of an analytic solution of the system are found. Consideration is given to the case of an arbitrary number of space variables. Bibliography: 4 titles.

[1] P. D. Lake, “Integraly nelineinykh evolyutsionnykh uravnenii i uedinennye volny”, Matematika, 13:5 (1969), 128–150 | MR

[2] C. S. Gardner, J. M. Green, M. D. Kruskal, R. M. Miura, “Method for solving the Korteweg–de Vries equation”, Phys. Rev. Lett., 19:19 (1967), 1095–1097 | DOI | Zbl

[3] M. J. Ablowitz, D. J. Kaup, A. C. Newell, H. Segur, “Nonlinear-Evolution Equations of Physical Significance”, Phys. Rev. Lett., 31:2 (1973), 125–127 | DOI | MR

[4] V. K. Melnikov, Ob odnom semeistve vpolne integriruemykh evolyutsionnykh sistem, Preprint OIYaI R2-10966, Dubna, 1977 | Zbl