Application of a Nonlinear WKB Method to the Korteweg–DeVries Equation
Robert M. Miura, Martin D. Kruskal
Source abstract
The WKB method used in quantum mechanics for solving linear second order ordinary differential equations is generalized to apply to nonlinear partial differential equations. In particular, this nonlinear WKB method, which is similar to the averaging method due to Whitham, is used to study nearly-periodic solutions of the Korteweg–deVries equation when the dispersion parameter is small. The emphasis of this paper is on a detailed analysis of the leading-order problem arising from the application of the nonlinear WKB method. An explicit representation of the leading-order solution is obtained in terms of unknown functions whose qualitative properties are studied. These unknown functions are governed by a first order system of nonlinear partial differential equations which is of hyperbolic type.
Evidence graph
No public relationships recorded yet.
Integrity note: This page is a factual metadata record created by deterministic ingestion. It is not a claim that the work moves a mathematical frontier or has been independently verified.