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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.

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