Nonlocal nonlinear Schrödinger equations and their soliton solutions
Date
2018-05-04
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Source Title
Journal of Mathematical Physics
Print ISSN
0022-2488
Electronic ISSN
Publisher
American Institute of Physics
Volume
59
Issue
5
Pages
051501-1 - 051501-17
Language
English
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Abstract
We study standard and nonlocal nonlinear Schrödinger (NLS) equations obtained from the coupled NLS system of equations (Ablowitz-Kaup-Newell-Segur (AKNS) equations) by using standard and nonlocal reductions, respectively. By using the Hirota bilinear method, we first find soliton solutions of the coupled NLS system of equations; then using the reduction formulas, we find the soliton solutions of the standard and nonlocal NLS equations. We give examples for particular values of the parameters and plot the function |q(t, x)|2 for the standard and nonlocal NLS equations.