Existence of Ground State and Excited Spinning $Q$-Vortex Solitons on Finite Domains
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908819718668288 |
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| author | Brumelot, Caroline Medina, Luciano |
| author_facet | Brumelot, Caroline Medina, Luciano |
| contents | 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 $ω$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_07676 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of Ground State and Excited Spinning $Q$-Vortex Solitons on Finite Domains Brumelot, Caroline Medina, Luciano Mathematical Physics 35J20, 35Q55, 35Q60, 65N30 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 $ω$, 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. |
| title | Existence of Ground State and Excited Spinning $Q$-Vortex Solitons on Finite Domains |
| topic | Mathematical Physics 35J20, 35Q55, 35Q60, 65N30 |
| url | https://arxiv.org/abs/2602.07676 |