A variational method to study the Zakharov equation. (English) Zbl 1119.35086
The author applies Ritz variational principle based on the Zakharov-Lagrangian to solve the Zakharov equation, which may be a model for both linear and nonlinear evolution of some instabilities in a wave system or flow. Spatial variance of trial function was assumed a priori, wile time dependence of its parameters was subject to optimization. The crucial point, finding an appropriate trial function, was solved by introducing the variability to parameters of a stationary solution of the Zakharov equation.
Reviewer: Messoud A. Efendiev (Berlin)
MSC:
35Q55 | NLS equations (nonlinear Schrödinger equations) |
35A15 | Variational methods applied to PDEs |
82D10 | Statistical mechanics of plasmas |