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Related papers: Klein-Gordon-Maxwell System in a bounded domain

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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 study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many standing…

Analysis of PDEs · Mathematics 2019-12-03 Monica Lazzo , Lorenzo Pisani

We study the class of nonlinear Klein-Gordon-Maxwell systems describing a standing wave (charged matter field) in equilibrium with a purely electrostatic field. We improve some previous existence results in the case of an homogeneous…

Analysis of PDEs · Mathematics 2009-12-01 Antonio Azzollini , Lorenzo Pisani , Alessio Pomponio

We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static…

Analysis of PDEs · Mathematics 2019-12-03 Monica Lazzo , Lorenzo Pisani

We prove existence and uniform bounds for electrostatic Klein-Gordon-Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is small in a quantified sense.

Analysis of PDEs · Mathematics 2010-12-17 Olivier Druet , Emmanuel Hebey

In this paper we consider the Klein-Gordon-Maxwell system in the electrostatic case, assuming the fall-off large-distance requirement on the gauge potential. We are interested in proving the existence of finite energy (and finite charge)…

Analysis of PDEs · Mathematics 2020-09-02 Antonio Azzollini

We are interested to the existence of standing waves for the nonlinear Klein Gordon equation {\epsilon}^2{\box}{\psi} + W'({\psi}) = 0 in a bounded domain D. The main result of this paper is that, under suitable growth condition on W, for…

Analysis of PDEs · Mathematics 2010-12-30 Marco G. Ghimenti , Carlo R. Grisanti

In this paper, we study the standing wave solutions of Klein--Gordon equation with logarithmic nonlinearity. The existence of the standing wave solution related to the ground state $\phi_0(x)$ is obtained. Further, we prove the instability…

Analysis of PDEs · Mathematics 2024-02-20 Lijia Han , Yue Qiu , Xiaohong Wang

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

In this paper, we consider the wave equation for the Laplace operator with potential, initial data, and nonhomogeneous Dirichlet boundary condition. We establish a weak solution by using traces and extension domains. We also establish the…

Analysis of PDEs · Mathematics 2025-01-28 Michael Ruzhansky , Alibek Yeskermessuly

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point…

Analysis of PDEs · Mathematics 2019-11-12 Elek Csobo , François Genoud , Masahito Ohta , Julien Royer

The stability of topological solitary waves and pulses in one-dimensional nonlinear Klein-Gordon systems is revisited. The linearized equation describing small deviations around the static solution leads to a Sturm-Liouville problem, which…

Pattern Formation and Solitons · Physics 2022-11-30 Pablo Rabán , Renato Alvarez-Nodarse , Niurka R. Quintero

In this work we prove the existence of standing-wave solutions to the scalar non-linear Klein-Gordon equation in dimension one and the stability of the ground-state, the set which contains all the minima of the energy constrained to the…

Analysis of PDEs · Mathematics 2019-10-15 Daniele Garrisi

We analyze $L^2$-normalized solutions of nonlinear Schr\"odinger systems of Gross-Pitaevskii type, on bounded domains, with homogeneous Dirichlet boundary conditions. We provide sufficient conditions for the existence of orbitally stable…

Analysis of PDEs · Mathematics 2019-03-27 Benedetta Noris , Hugo Tavares , Gianmaria Verzini

We study nonlinear bound states, or solitary waves, in the Dirac-Maxwell system proving the existence of solutions in which the Dirac wave function is of the form $\phi(x,\omega)e^{-i\omega t}$, $\omega\in(-m,\omega_*)$, with some…

Mathematical Physics · Physics 2017-09-28 Andrew Comech , David Stuart

We consider a system of two coupled non-linear Klein-Gordon equations. We show the existence of standing waves solutions and the existence of a Lyapunov function for the ground state.

Analysis of PDEs · Mathematics 2011-05-31 Daniele Garrisi

We investigate the stability and long-term behavior of spatially periodic plane waves in the complex Klein-Gordon equation under localized perturbations. Such perturbations render the wave neither localized nor periodic, placing its…

Analysis of PDEs · Mathematics 2026-03-03 Emile Bukieda , Louis Garénaux , Björn de Rijk

We seek to introduce a mathematical method to derive the Klein-Gordon equation and a set of relevant laws strictly, which combines the relativistic wave functions in two inertial frames of reference. If we define the stationary state wave…

Analysis of PDEs · Mathematics 2010-11-08 Guangqing Bi , Yuekai Bi

Let (M,g) be a smooth compact, n dimensional Riemannian manifold, n=3,4 with smooth n-1 dimensional boundary. We search the positive solutions of the singularly perturbed Klein Gordon Maxwell Proca system with homogeneous Neumann boundary…

Analysis of PDEs · Mathematics 2014-11-04 Marco Ghimenti , Anna Maria Micheletti

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For a system of nonlinear Klein-Gordon equations, a systematic analysis of the time evolution for their spatially uniform solutions has been performed…

Mathematical Physics · Physics 2023-10-03 Yasuhiro Takei , Yoritaka Iwata
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