Exactly solvable Gross-Pitaevskii type equations
Abstract
TWe suggest a method to construct exactly solvable Gross-Pitaevskii type equations, especially the variable-coefficient high-order Gross-Pitaevskii type equations. We show that there exists a relation between the Gross-Pitaevskii type equations. The Gross-Pitaevskii equations connected by the relation form a family. In the family one only needs to solve one equation and other equations in the family can be solved by a transform. That is, one can construct a series of exactly solvable Gross-Pitaevskii type equations from one exactly solvable Gross-Pitaevskii type equation. As examples, we consider the family of some special Gross-Pitaevskii type equations: the nonlinear Schr\"odinger equation, the quintic Gross-Pitaevskii equation, and cubic-quintic Gross-Pitaevskii equation. We also construct the family of a kind of generalized Gross-Pitaevskii type equation.
Cite
@article{arxiv.2004.09972,
title = {Exactly solvable Gross-Pitaevskii type equations},
author = {Yuan-Yuan Liu and Wen-Du Li and Wu-Sheng Dai},
journal= {arXiv preprint arXiv:2004.09972},
year = {2021}
}