TY - JOUR
T1 - On the reflection of solitons of the cubic nonlinear Schrödinger equation
AU - Katsaounis, Theodoros
AU - Mitsotakis, Dimitrios
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: Victoria University of Wellington[208964]
PY - 2016/7/5
Y1 - 2016/7/5
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/619215
UR - https://arxiv.org/abs/1602.04424
UR - http://www.scopus.com/inward/record.url?scp=84979085492&partnerID=8YFLogxK
U2 - 10.1002/mma.4070
DO - 10.1002/mma.4070
M3 - Article
SN - 0170-4214
VL - 41
SP - 1013
EP - 1018
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 3
ER -