The Gross-Pitaevskii equation: B\"acklund transformations and admitted solutions
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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