International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 22, Pages 3703-3709
A variational method to study the Zakharov equation
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.