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

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Abstract

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.

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Barna, I. F., Pocsai, M. A., & Mátyás, L. (2018). Self-Similarity Analysis of the Nonlinear Schrödinger Equation in the Madelung Form. Advances in Mathematical Physics, 2018. https://doi.org/10.1155/2018/7087295

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