Ground States of the Nonlinear Schrödinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition

2025/05/07 by Duboscq, Romain, Durand-Simonnet, Élio, Coz, Stefan Le
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.04250

Abstract

We consider the stationary nonlinear Schrödinger equation set on a tadpole graph with a repulsive delta vertex condition between the loop and the tail of the tadpole. We establish the existence of an action ground state when the size of the loop is either very small or very large. Our analysis relies on variational arguments, such as profile decomposition. When it exists, we study the shape of the ground state using ordinary differential equations arguments, such as the study of period functions. The theoretical results are completed with a numerical study.

Citations

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Related

• Ground States for the Defocusing Nonlinear Schrödinger Equation on Non-Compact Metric Graphs
• On the notion of ground state for nonlinear Schrödinger equations on metric graphs
• Standing waves on a flower graph
• Ground States for the Nonlinear Schrödinger Equation on Open Books and Dimensional Reduction to Metric Graphs
• Stability transitions of NLS action ground-states on metric graphs