Numerical study of quintic NLS equation with defect

Abstract

In this work, we numerically investigate how a defect can affect the behavior of traveling explosive solutions of quintic NLS equation in the one-dimensional case. Our numerical method is based on a Crank-Nicolson scheme in the time, finite difference method in space including a Perfectly Matched Layer (PML) treatment for the boundary conditions. It is observed that the defect splits the incident wave in one reflected part and one transmitted part; hence the dynamics of the solution may be changed and the blow-up may be prevented depending on the values of the defect amplitude \(Z\). Moreover, it is numerically found that the defect can be considered as a barrier for large \(Z\).