D.N.: Analytical solutions to a class of nonlinear Schrödinger equations with PT like potentials

We present closed form solutions to a certain class of one- and two-dimensional nonlinear Schrödinger 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 Schrödinger equation with a non-separable complex potential. PACS numbers: 03.65.Ge, 02.60.Lj, 11.30.Er, 42.65.Tg, 42.65.Wi (Some figures in this article are in colour only in the electronic version) 1