Normalized ground state solutions of Schrödinger-KdV system in R3

In this paper, we study the coupled Schrödinger-KdV system -Δu+λ1u=u3+βuvinR3,-Δv+λ2v=12v2+12βu2inR3subject to the mass constraints ∫R3|u|2dx=a,∫R3|v|2dx=b,where a,b>0 are given constants, β>0, and the frequencies λ1,λ2 arise as Lagrange multipliers. The system exhibits L2-supercritical growth...

Full description

Saved in:
Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 75; no. 6
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.12.2024
Subjects
Constraints
Ground state
Lagrange multiplier
Online AccessGet full text
ISSN0044-2275
1420-9039
DOI10.1007/s00033-024-02330-8

Cover

More Information
Summary:In this paper, we study the coupled Schrödinger-KdV system -Δu+λ1u=u3+βuvinR3,-Δv+λ2v=12v2+12βu2inR3subject to the mass constraints ∫R3|u|2dx=a,∫R3|v|2dx=b,where a,b>0 are given constants, β>0, and the frequencies λ1,λ2 arise as Lagrange multipliers. The system exhibits L2-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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-024-02330-8