Analytical solutions to a class of nonlinear Schrödinger equations with {\cal PT} -like potentials

Abstract

We present closed form solutions to a certain class of one- and two-dimensional nonlinear Schrodinger equations involving potentials with broken and unbroken PT symmetry. In the one-dimensional case, these solutions are given in terms of Jacobi elliptic functions, hyperbolic and trigonometric functions. Some of these solutions are possible even when the corresponding PT-symmetric potentials have a zero threshold. In two-dimensions, hyperbolic secant type solutions are obtained for a nonlinear Schrodinger equation with a nonseparable complex potential.