一个非线性Gross-Pitaevskii方程的行波解  

Traveling Waves for a Nonlinear Gross-Pitaevskii Equation

作　　者：杨滨宾 

机构地区：[1]上海理工大学理学院,上海

出　　处：《理论数学》2024年第4期197-206,共10页Pure Mathematics

摘　　要：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,我们的目的就是对局部相互作用提供一些条件,从而得到存在这样的一组行波解。我们的结论主要通过证明能量泛函在具有固定的动量时有最小值,该过程中主要运用集中紧性原理和一致先验估计。In this paper, we mainly discuss the traveling waves of a nonlinear Gros-Pitaevskii equation in one-dimensional case. Our aim is to provide some conditions for local interactions, so as to obtain the existence of traveling waves. Our conclusion is mainly based on the proof that the energy functional has a minimum value when it has a fixed momentum, which mainly uses the concentrated compactness principle and the uniform prior estimation.

关 键 词：非线性薛定谔方程 行波解 暗孤子 无穷远处非零 

分 类 号：TM7[电气工程—电力系统及自动化]