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arXiv · 2502.21200

Existence and orbital stability of standing-wave solutions of the NLS-log equation on a tadpole graph

Jaime Angulo Pava·Andrés Gerardo Pérez Yépez
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Abstract

This work aims to study some dynamical aspects of the nonlinear logarithmic Schr\"odinger equation (NLS-log) on a tadpole graph, namely, a graph consisting of a circle with a half-line attached at a single vertex. By considering Neumann-Kirchhoff boundary conditions at the junction we show the existence and the orbital stability of standing wave solutions with a profile determined by a positive single-lobe state. Via a splitting-eigenvalue method, we identify the Morse index and the nullity index of a specific linearized operator around a positive singlelobe state. To our knowledge, the results contained in this paper are the first to study the (NLS-log) on tadpole graphs. In particular, our approach has the prospect of being extended to study stability properties of other bound states for the (NLS-log) on a tadpole graph or other non-compact metric graph such as a looping-edge graphs.

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Jaime Angulo Pava, Andrés Gerardo Pérez Yépez. 2025-02-28. Existence and orbital stability of standing-wave solutions of the NLS-log equation on a tadpole graph. https://arxiv.org/abs/2502.21200

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