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.


35Q53 KdV equations (Korteweg-de Vries equations)
35L65 Hyperbolic conservation laws
35A22 Transform methods (e.g., integral transforms) applied to PDEs
34L99 Ordinary differential operators
49R50 Variational methods for eigenvalues of operators (MSC2000)


Zbl 0283.35018
Full Text: DOI


[1] DOI: 10.1063/1.1664700 · Zbl 0283.35018
[2] DOI: 10.1098/rspa.1965.0019 · Zbl 0125.44202
[3] DOI: 10.1103/PhysRevLett.19.1095
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