Miura, Robert M.; Gardner, Clifford S.; Kruskal, Martin D. Korteweg-de Vries equation and generalizations. II: Existence of conservation laws and constants of motion. (English) Zbl 0283.35019 J. Math. Phys. 9, No. 8, 1204-1209 (1968). 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. Cited in 9 ReviewsCited in 262 Documents 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) PDF BibTeX XML Cite \textit{R. M. Miura} et al., J. Math. Phys. 9, 1204--1209 (1968; Zbl 0283.35019) Full Text: DOI References: [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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.