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Korteweg-de Vries equation and generalizations. II: Existence of conservation laws and constants of motion. (English) Zbl 0283.35019
Summary: With extensive use of the nonlinear transformations presented in Paper I of the series by the first author [J. Math. Phys. 9, No. 8, 1202--1204 (1968; Zbl 0283.35018)], a variety of conservation laws and constants of motion are derived for the Korteweg--de Vries and related equations. A striking connection with the Sturm--Liouville eigenvalue problem is exploited.

35Q53KdV-like (Korteweg-de Vries) equations
35L65Conservation laws
35A22Transform methods (PDE)
34L99Ordinary differential operators
49R50Variational methods for eigenvalues of operators (MSC2000)
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