A variational method to study the Zakharov equation

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.