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Existence and stability of traveling waves for nonlinear Schr\"odinger equations with van der Waals type potentials
Lu Hui, Wu Dan *
School of Mathematics, University of Hunan, Changsha 410082
*Correspondence author
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Funding: ***基金（No.00000000）, ***基金（No.00000000）
Opened online:19 May 2023
Accepted by: none
Citation: Lu Hui, Wu Dan.Existence and stability of traveling waves for nonlinear Schr\"odinger equations with van der Waals type potentials[OL]. [19 May 2023] http://en.paper.edu.cn/en_releasepaper/content/4760739
 
 
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.
Keywords:Variational method; Nonlinear Schrodinger equation; Traveling wave solution; Orbital stability
 
 
 

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