International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3703-3709

A variational method to study the Zakharov equation

Arun Kumar

Department of Mathematics, Government College, Kota (Raj) 324001, India

Received 7 February 2005; Revised 4 August 2005

Copyright © 2005 Arun Kumar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A variational method given by Ritz has been applied to the Zakharov equation to construct an analytical solution. The solution of Zakharov equation gives a good description of both linear and nonlinear evolutions of instabilities generated in waves due to modulation. The spatially periodic trial function is chosen in the form of combination of Jacobian elliptic functions with the dependence of its parameters subject to optimization. This Zakharov equation is reduced to nonlinear Schrödinger equation in the static limit.