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arXiv · 2004.09972

Exactly solvable Gross-Pitaevskii type equations

Yuan-Yuan Liu·Wen-Du Li·Wu-Sheng Dai
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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.

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Yuan-Yuan Liu, Wen-Du Li, Wu-Sheng Dai. 2020-04-20. Exactly solvable Gross-Pitaevskii type equations. https://doi.org/10.1088/2399-6528%2Fabda12

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