具有范德华势的非线性薛定谔方程稳定行波解的存在性
Existence and stability of traveling waves for nonlinear Schr\"odinger equations with van der Waals type potentials
本文研究了具有范德华势的半伪相对论薛定谔方程的行波解的存在性和一些稳定性结果。基于变分法,本文利用集中紧性原理研究相应的约束极小化问题,推出了极小化问题的最小元的存在性,从而得到欧拉-拉格朗日方程的准基态的存在性。 进一步,本文证明了行波解具有轨道稳定性。
In this paper, we study the existence and some stability results of traveling wave solutions of the semi-pseudo-relativistic Schr\"odinger equation with van der Waals potential. Based on the variational method, we study the corresponding constraint minimization problem by using the principle of concentrated compactness, and deduce the existence of the global minimizer of the minimization problem, thus obtaining the existence of the boosted ground state of Euler-Lagrange equaton. Furthermore, it is proved that the traveling wave solutions are orbitally stable.
卢慧、吴丹
物理学数学
变分法非线性薛定谔方程行波解轨道稳定性
Variational methodNonlinear Schrodinger equationTraveling wave solutionOrbital stability
卢慧,吴丹.具有范德华势的非线性薛定谔方程稳定行波解的存在性[EB/OL].(2023-05-19)[2025-08-04].http://www.paper.edu.cn/releasepaper/content/202305-139.点此复制
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