1969•Journal of Mathematical PhysicsRequires access

Korteweg-de Vries Equation and Generalizations. III. Derivation of the Korteweg-de Vries Equation and Burgers Equation

C. H. Su, Clifford S. Gardner

Abstract

The Korteweg-de Vries equation and the Burgers equation are derived for a wide class of nonlinear Galilean-invariant systems under the weak-nonlinearity and long-wavelength approximations. The former equation is shown to be a limiting form for nonlinear dispersive systems while the latter is a limiting form for nonlinear dissipative systems.

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Key concepts: Burgers' equation, Korteweg–de Vries equation, Dispersionless equation, Kadomtsev–Petviashvili equation, Nonlinear system, Mathematics, Dissipative system, Mathematical physics