Model and numerical method for soliton propagation through thermal medium based on nonlinear Schrödinger and heat transfer equations

Abstract

We present a mathematical model and numerical method for simulating soliton propagation through thermal medium. The model is developed based on the nonlinear Schrödinger (NLS) equation coupled with a heat transfer equation. The well-posedness of the model and stability of the solution are analyzed. We then develop a second-order accurate finite difference scheme for solving this problem and prove the numerical solution to be bounded in l∞ norm. Furthermore, the scheme is proved to be second-order convergent in l2 norm. Numerical examples are given to verify the model and test the accuracy of the numerical scheme for simulating soliton propagations through the thermal medium.