Numerical study of quintic NLS equation with defects

Laurent Di Menza , Olivier Goubet (1) , Emna Hamraoui (1)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

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.

Mots clés: Quintic NLS equation delta-function explosive traveling solution blow-up; Quintic NLS equation; delta-function; explosive traveling solution; blow-up

Domaines: Mathématiques [math]

Laurent Di Menza, Olivier Goubet, Emna Hamraoui. Numerical study of quintic NLS equation with defects. North-Western European Journal of Mathematics, 2023, 9 (2023), pp.55-75. ⟨hal-03847204⟩