Numerical Simulations of the Envelope Created by Nearly Bichromatic Waves

Nohara, B.T., Saigo, T.
Tokyo Nonlinear Analysis Research Center, Musashi Institute of Technology, Tokyo, Japan

In this paper, we present the stability analysis numerically using FEMLAB.

We use FEMLAB for solving PDEs (Partial Differential Equation) and obtain numerical solutions. We show a case study of avoiding perturbation problems arising in some PDEs derived by “nearly bichromatic waves” using FEMLAB.

Coefficients of equations determine whether solutions are stable. In analyzing the stability of the envelope equations with small higher-order terms, we study such equations numerically using the known results of the nonlinear Schröodinger equation.

We have time-series portraits of envelopes created by nearly bichromatic waves. Comparing portraits of the solutions, we find that the equation with small higher-order terms is stable for perturbation if the difference between the nonlinear Schröodinger equation and the equation with small higher-order terms is small.