## Variational approach to nonlinear evolution of modulational instability using one-dimensional Zakharov equations

The Ritz variational method has been applied to the Zakharov equations to construct a model for the nonlinear evolution of modulational instability. Spatiotemporal chaos and nonlinear evolution patterns of the modulational instability are investigated theoretically by choosing an appropriate trial function for the field for periodic field and density perturbations. The spatially periodic field trial function was chosen in the form of a combination of Jacobian elliptic functions with the dependence of its parameters subject to optimization. It is found that these evolutions are quite sensitive to the initial conditions, recurrence is broken up and a chaotic state develops. Theoreticalmore »