The Gross-Pitaevskii equation: B\"acklund transformations and admitted solutions
Mathematical Physics
2019-01-04 v2 Analysis of PDEs
math.MP
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.
Cite
@article{arxiv.1803.09228,
title = {The Gross-Pitaevskii equation: B\"acklund transformations and admitted solutions},
author = {Sandra Carillo and Federico Zullo},
journal= {arXiv preprint arXiv:1803.09228},
year = {2019}
}
Comments
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