The Korteweg-de Vries equation and related evolution equations
Abstract
The Korteweg-de Vries (KdV) equation provides a simple and useful model for describing the long-time evolution of certain wave phenomena. An approach is shown for deriving the conservation laws with the aid of a generating function. A brief review is given of a method for solving the initial value problem. A derivation of the KdV equation as it arises in the Fermi-Pasta-Ulam problem is also presented.
- Publication:
-
In: Nonlinear wave motion. (A75-14987 04-70) Providence
- Pub Date:
- 1974
- Bibcode:
- 1974ams..conf...61K
- Keywords:
-
- Boundary Value Problems;
- Conservation Laws;
- Nonlinear Equations;
- Time Dependence;
- Wave Equations;
- Asymptotic Methods;
- Differential Equations;
- Function Generators;
- Long Term Effects;
- Wentzel-Kramer-Brillouin Method;
- Physics (General)