Nonlocal Nonlinear Schr\"odinger Equations and Their Soliton Solutions
By M. Gurses, Aslı Pekcan. 2017
202 citations recorded by the source corpus.
We study standard and nonlocal nonlinear Schrodinger (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.
Subfields: Atomic and Molecular Physics, and Optics, Modeling and Simulation, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/0d1813542ff1f3e46ba2bb6bc954f310c5265806
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In Atomic and Molecular Physics, and Optics
In Modeling and Simulation
In Statistical and Nonlinear Physics
Citations in the corpus
- Long-time asymptotics for the nonlocal nonlinear Schrödinger equation with step-like initial data (2021, methodology): “The one-, two- and three-soliton solutions are obtained via the Hirota’s direct method in [25] whereas in [15], the decaying one-soliton solution is obtained in terms of a double Wronskian.”