Evolution of Modulational Instability in Non-linear Hirota Types Equation

Abstract

The Time Dependent Variational Approach (TDVA) is applied to estimate the modulational instability (MI) for Non-Linear Hirota type equations. This approach is new to obtain the nonlinear dispersion relation (NDR) for such equations. The classical modulational instability criterion is nascent and it establishes many prospective for the MI domain because of the generalized dispersion relation. Analyzing the Non Linear Partial Differential Equations, we rederive the classical modulational instability criterion.