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arXiv · 2602.07676

Existence of Ground State and Excited Spinning $Q$-Vortex Solitons on Finite Domains

Caroline Brumelot·Luciano Medina
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Abstract

We establish the existence of spinning $Q$-vortex solitons in a complex scalar field theory with a sextic potential on a finite domain. By reducing the governing equation to a nonlinear boundary value problem, we use variational methods to prove the existence of at least two distinct types of solutions: a ground state solution obtained via constrained minimization and an excited state of the saddle-point type obtained via the Mountain Pass Theorem. We derive bounds for the angular frequency $\omega$, the wave amplitude, and the domain size $P$, and provide explicit estimates for the exponential decay of the solutions. Furthermore, we implement a spectral-Galerkin formulation to numerically compute the profiles of fundamental $Q$-vortices, illustrating the saturation behavior of the soliton's amplitude and the asymptotic dependence of the frequency on a prescribed reduced norm and vortex winding number, as well as verifying the theoretical results and visualizing the topological phase structure of the solutions.

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Caroline Brumelot, Luciano Medina. 2026-02-07. Existence of Ground State and Excited Spinning $Q$-Vortex Solitons on Finite Domains. https://arxiv.org/abs/2602.07676

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