The Gross-Pitaevskii equation: Bäcklund transformations and admitted solutions

Published 25 Mar 2018 in math-ph, math.AP, and math.MP | (1803.09228v2)

Abstract: B\"acklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of B\"acklund transformations admitted by this equation are constructed. Schwartzian derivative as well as its invariance properties turn out to represent a key tool in the present investigation. Examples and explicit solutions of the Gross-Pitaevskii equation are obtained.

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