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

Imre F. Barna, Mihály A. Pocsai and L. Mátyás

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

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.

Date: 2018
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https://doi.org/10.1155/2018/7087295

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:7087295

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