非线性Goss-Pitaevskii方程的行波解的存在性

Existence of Traveling Waves Solutions for the Nonlinear Goss-Pitaevskii Equations

本文主要讨论一个非线性Gross-Pitaevskii方程在一维情形下的行波解,我们建立了与最小化问题相关的欧拉–拉格朗日方程,从而证明行波解的存在性,更准确地说,建立了由动量参数化的解族的存在性。

This article mainly discusses the traveling wave solution of a nonlinear Gross-Pitaevskii equation in one-dimensional case.We establish the Euler-Lagrange equation related to the minimization problem,which is crucial for proving the existence of traveling wave solutions.More precisely,the existence of a family of solutions parameterized by momentum is established.