一类 Schrödinger 方程组驻波解的存在性与渐近性——献给邓引斌教授 70 寿辰

Abstract

Abstract:

This paper studies standing wave solutions for a class of nonlinear Schrödinger system (involving three-wave interactions) that describe the Raman amplification model in plasmas within the non-focusing regime. For spatial dimension $N=4$, the existence and nonexistence of ground state solutions are established by means of variational methods and compactness analysis. Furthermore, the asymptotic behavior of the ground states under synchronized mass variations is characterized, and a precise correspondence with the Thomas-Fermi limit is established. This work extends and generalizes the results of [Forcella L, Luo X, Yang T, et al. arXiv: 2210.07643] to higher dimensions.

Key words: NLS system, standing waves, ground state solution, asymptotic behavior

CLC Number:

O175.23

Longge Shi, Xiaolong Yang. Existence and Asymptotic Behavior of Standing Wave Solutions for a Class of Schrödinger Systems[J].Acta mathematica scientia,Series A, 2026, 46(4): 1513-1528.

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References 25

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Existence and Asymptotic Behavior of Standing Wave Solutions for a Class of Schrödinger Systems

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