Exact solutions of a two-dimensional nonlinear Schrödinger equation

Abstract In the present study, we converted the resulting nonlinear equation for the evolution of weakly nonlinear hydrodynamic disturbances on a static cosmological background with self-focusing in a two-dimensional nonlinear Schrodinger (NLS) equation. Applying the function transformation method, the NLS equation was transformed to an ordinary differential equation, which depended only on one function ξ and can be solved. The general solution of the latter equation in ζ leads to a general solution of NLS equation. A new set of exact solutions for the two-dimensional NLS equation is obtained.

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