一个非线性Gross-Pitaevskii方程的行波解
Traveling Waves for a Nonlinear Gross-Pitaevskii Equation
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。
Abstract: 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.
文章引用：杨滨宾. 一个非线性Gross-Pitaevskii方程的行波解[J]. 理论数学, 2024, 14(4): 197-206. https://doi.org/10.12677/pm.2024.144127

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