On the reflection of solitons of the cubic nonlinear Schrödinger equation

Theodoros Katsaounis, Dimitrios Mitsotakis

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In this paper, we perform a numerical study on the interesting phenomenon of soliton reflection of solid walls. We consider the 2D cubic nonlinear Schrödinger 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.
Original languageEnglish (US)
Pages (from-to)1013-1018
Number of pages6
JournalMathematical Methods in the Applied Sciences
Issue number3
StatePublished - Jul 5 2016

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