Korteweg-de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion

1968/08/01 by Robert M. Miura, Clifford S. Gardner, Martin D. Kruskal · 18 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Quantum chaos and dynamical systems #Conservation law #Korteweg–de Vries equation #Eigenvalues and eigenvectors #Mathematics #Nonlinear system #Connection (principal bundle) #Motion (physics) #Series (stratigraphy) #Mathematical physics #Variety (cybernetics) #Constant (computer programming) #Mathematical analysis #Classical mechanics #Physics #Geometry #Computer science #Quantum mechanics

paper · doi:10.1063/1.1664701

openalex publication_date 1968/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

With extensive use of the nonlinear transformations presented in Paper I of the series, 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.

Citations

• Method for Solving the Korteweg-deVries Equation

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