Numerical study of quintic NLS equation with defects
Résumé
In this work, we numerically investigate how a defect can affect the behavior of traveling explosive solutions of quintic NLS equation in the onedimensional 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.
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