Self-similarity analysis of the non-linear Schr\"odinger equation in the Madelung form

Imre F. Barna; Mihály A. Pocsai; L. Mátyás

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arXiv · 1804.06274

Self-similarity analysis of the non-linear Schr\"odinger equation in the Madelung form

Imre F. Barna·Mihály A. Pocsai·L. Mátyás

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Abstract

In the present study a particular case of Gross-Pitaevskii or non-linear Schr\"odinger 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 solutions, a larger coefficient of the nonlinear term yields stronger deviation of the solution from the linear case.

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Imre F. Barna, Mihály A. Pocsai, L. Mátyás. 2018-04-17. Self-similarity analysis of the non-linear Schr\"odinger equation in the Madelung form. https://arxiv.org/abs/1804.06274

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