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Related papers: Non-Topological Solitons in $3+1$ Dimensions

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We consider a system of nonlinear Klein-Gordon equations with quadratic interaction in two and three space dimensions. The strong instability of standing wave solutions is studied for the system without assuming the mass resonance…

Analysis of PDEs · Mathematics 2025-09-09 Masahito Ohta

The solitary waves of massive (1+1)-dimensional nonlinear S^N-sigma models are unveiled. It is shown that the solitary waves in these systems are in one-to-one correspondence with the separatrix trajectories in the repulsive N-dimensional…

High Energy Physics - Theory · Physics 2010-02-10 A. Alonso Izquierdo , M. Á. González León , M. de la Torre Mayado

We consider the damped nonlinear Klein-Gordon equation: \begin{align*} \partial_{t}^2u-\Delta u+2\alpha \partial_{t}u+u-|u|^{p-1}u=0, \ & (t,x) \in \mathbb{R} \times \mathbb{R}^d, \end{align*} where $\alpha>0$, $1\leq d\leq 5$ and energy…

Analysis of PDEs · Mathematics 2026-02-03 Kenjiro Ishizuka

Tachyons or hypothetical faster-than-light (FTL) particles would fail the principle of causality. Such particles may only be imagined when they have no energy and momentum and, thus, no observable interaction. In this paper, we show that…

General Relativity and Quantum Cosmology · Physics 2024-04-05 Mohammad Mohammadi

The (1+1)-dimensional Sine-Gordon equation passes integrability tests commonly applied to nonlinear evolution equations. Its soliton solutions are obtained by a Hirota algorithm. In higher space-dimensions, the equation does not pass these…

Exactly Solvable and Integrable Systems · Physics 2014-04-25 Yair Zarmi

The Sine-Gordon equation in (1+2) dimensions has N-soliton solutions that propagate at velocities that are lower than the speed of light (c = 1), for any N greater tha or equal to 1. A first integral of the equation, which vanishes…

Exactly Solvable and Integrable Systems · Physics 2014-04-25 Yair Zarmi

We study finite energy static solutions to a global symmetry breaking Goldstone model described by an isovector scalar field in D+1 spacetime dimensions. Both topologically stable multisolitons with arbitrary winding numbers, and zero…

High Energy Physics - Theory · Physics 2009-11-13 Eugen Radu , D. H. Tchrakian

We consider the dynamics of even solutions of the one-dimensional nonlinear Klein-Gordon equation $\partial_t^2 \phi - \partial_x^2 \phi + \phi - |\phi|^{2\alpha} \phi =0$ for $\alpha>1$, in the vicinity of the unstable soliton $Q$. Our…

Analysis of PDEs · Mathematics 2019-04-01 Michal Kowalczyk , Yvan Martel , Claudio Muñoz

Despite the fact that it is not integrable, the 1 + 2-dimensional Sine-Gordon equation has N-soliton solutions, whose velocities are lower than the speed of light (c = 1), for all N greater than or equal to 1. Based on these solutions, a…

Exactly Solvable and Integrable Systems · Physics 2015-06-19 Yair Zarmi

We construct numerical solutions for non-topological solitons in three-dimensional U(1)-gauged ${\cal N}=2$ supergravity. We find the region of the solutions showing with the BTZ mass, the angular momentum and the magnetic flux and discuss…

General Relativity and Quantum Cosmology · Physics 2016-08-31 Yoshinori Cho , Kenji Sakamoto , Kiyoshi Shiraishi

We obtain explicit characterization of spectral and orbital stability of solitary wave solutions to the $\mathbf{U}(1)$-invariant Klein--Gordon equation in one spatial dimension coupled to an anharmonic oscillator. We also give the complete…

Analysis of PDEs · Mathematics 2020-12-09 Andrew Comech , Elena A. Kopylova

We provide a review of non-topological solitonic solutions arising in theories with a complex scalar field and global or gauge $U(1)$-symmetry. It covers Q-balls, homogeneous charged scalar condensates, and nonlinear localized holes and…

High Energy Physics - Theory · Physics 2020-04-22 Emin Nugaev , Andrey Shkerin

The first analytic topologically non-trivial solutions in the (3+1)-dimensional gauged non-linear sigma model representing multi-solitons at finite volume with manifest ordered structures generating their own electromagnetic field are…

High Energy Physics - Theory · Physics 2019-06-17 Fabrizio Canfora , Seung Hun Oh , Aldo Vera

This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…

Analysis of PDEs · Mathematics 2008-12-17 Pietro d'Avenia , Lorenzo Pisani , Gaetano Siciliano

We introduce a setting based on the one-dimensional (1D) nonlinear Schroedinger equation (NLSE) with the self-focusing (SF) cubic term modulated by a singular function of the coordinate, |x|^{-a}. It may be additionally combined with the…

Pattern Formation and Solitons · Physics 2015-06-04 Olga V. Borovkova , Valery E. Lobanov , Boris A. Malomed

We obtain by dimensional reduction a $(1+1)$ supersymmetric system introduced in the description of ultracold quantum gases. The correct supercharges are identified and their algebra is constructed. Finally novel static self-dual solutions…

High Energy Physics - Theory · Physics 2014-01-21 Lucas Sourrouille

We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We…

Analysis of PDEs · Mathematics 2009-10-12 Claudio Bonanno

We look for three dimensional vortex-solutions, which have finite energy and are stationary solutions, of Klein-Gordon-Maxwell-Proca type systems of equations. We prove the existence of three dimensional cylindrically symmetric…

Analysis of PDEs · Mathematics 2017-05-24 Pietro d'Avenia , Jarosław Mederski , Alessio Pomponio

In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and…

Mathematical Physics · Physics 2013-12-20 Claudio Bonanno

A topological monopole-like field configuration exists for Yang-Mills gauge fields in a 4+1 dimensions. When the extra dimension is compactified to 3+1 dimensions with periodic lattice boundary conditions, these objects reappear in the low…

High Energy Physics - Theory · Physics 2009-11-07 Christopher T. Hill