The Gross-Pitaevskii equation: Bäcklund transformations and admitted solutions
arXiv:1803.09228 · doi:10.1007/s11587-018-0422-8
Abstract
Bäcklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of Bäcklund 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.
arXiv admin note: text overlap with arXiv:1711.04304 Authors' Answer: this article represents a further development of the previous one; thus, some crucial results are repeated for the reader convenience