Title: Nonlocal Nonlinear Schrödinger Equations and Their Soliton Solutions,
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.