Normalized ground state solutions of Schrödinger-KdV system in R3 Normalized ground state solutions

In this paper, we study the coupled Schrödinger-KdV system - Δ u + λ 1 u = u 3 + β u v in R 3 , - Δ v + λ 2 v = 1 2 v 2 + 1 2 β u 2 in R 3 subject to the mass constraints ∫ R 3 | u | 2 d x = a , ∫ R 3 | v | 2 d x = b , where a , b > 0 are given constants, β > 0 , and the frequencies λ 1 , λ 2...

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Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 75; no. 6
Main Authors Gao, Qian, Wang, Qun, Chang, Xiaojun
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2024
Subjects
Engineering
Mathematical Methods in Physics
Theoretical and Applied Mechanics
35J20
supercritical growth
Variational methods
35J60
Schrödinger-KdV System
35Q55
Normalized solutions
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Summary:In this paper, we study the coupled Schrödinger-KdV system - Δ u + λ 1 u = u 3 + β u v in R 3 , - Δ v + λ 2 v = 1 2 v 2 + 1 2 β u 2 in R 3 subject to the mass constraints ∫ R 3 | u | 2 d x = a , ∫ R 3 | v | 2 d x = b , where a , b > 0 are given constants, β > 0 , and the frequencies λ 1 , λ 2 arise as Lagrange multipliers. The system exhibits L 2 -supercritical growth. Using a novel constraint minimization approach, we demonstrate the existence of a local minimum solution to the system. Furthermore, we establish the existence of normalized ground state solutions.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-024-02330-8