On the construction of the exact analytic or parametric closed-form solutions of standing waves concerning the cubic nonlinear Schrodinger equation

摘要

We propose a new approach for the construction of the closed-form solutions of standing waves of the cubic nonlinear Schrodinger equation (NLS). Through appropriate functional transformations, we reduce the radially symmetric NLS into an Emden-Fowler equation whose solution results to the derivation of the closed forms of the standing waves. We also derive the necessary restrictions under which the derived solutions are admissible.