Physics

Nonlinear system

Mathematics

Mathematical physics

Quantum mechanics

Schrödinger equation

Breather

Classical mechanics

Nonlinear Schrödinger equation

Soliton

Journal of Mathematical Physics

We study standard and nonlocal nonlinear Schr\"{o}dinger (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.

Nonlocal nonlinear Schrödinger equations and their soliton solutions