Applied PDE Group
Nonlinear Partial Differential Equations in Fluid and Solid Mechanics

KM_Arxiv2016

On reflection of solitons of the cubic nonlinear Schrodinger equation

Th. Katsaounis, D. Mitsotakis, On reflection of solitons of the cubic nonlinear Schrodinger equation, to appear in Mathematical Methods in Applied Sciences​
Theodoros Katsaounis, Dimitrios Mitsotakis
soliton reflection, nonlinear Schrodinger
2016
In this paper we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schro ̈dinger equation as the underlying mathematical model and we use an implicit-explicit type Crank-Nicolson finite element scheme for its numerical solution. After verifying the perfect reflection of the solitons on a vertical wall, we present the imperfect reflection of a dark soliton on a diagonal wall