A linear and mass conservative scheme for the thermal soliton model based on nonlinear Schrödinger and heat transfer equations

Abstract

A fully decoupled and mass-conservative finite difference (FD) scheme is proposed for solving the thermal soliton model which consists of a nonlinear Schrödinger (NLS) equation and a heat transfer equation, simulating soliton propagation through thermal medium. The scheme is proved to be uniquely solvable and unconditionally stable. Furthermore, the numerical solution is shown to be bounded and second-order convergent in $l_{\infty }$ norm though the scheme has only the first-order spatial accuracy at the interfacial points. Several numerical examples are carried out to verify the theoretical analysis.