Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form

الملخص EN

In the present study a particular case of Gross-Pitaevskii or nonlinear Schrödinger equation is rewritten to a form similar to a hydrodynamic Euler equation using the Madelung transformation.

The obtained system of differential equations is highly nonlinear.

Regarding the solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.