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We consider the massive Dirac-Klein-Gordon system in two space dimensions. Under the non-resonace mass condition, we show that the solution is asymptotically free if the initial data are sufficiently small in a suitable weighted Sobolev…

Analysis of PDEs · Mathematics 2011-11-22 Masahiro Ikeda , Akihiro Shimomura , Hideaki Sunagawa

We construct a nonlinear multiparametric Klein-Gordon for complex and real fields with mass dimension depending on a real parameter $\alpha$ as $\delta = 2/(1+\alpha)$ where $\delta$ is the mass dimension of the fields. We show that there…

Quantum Physics · Physics 2024-12-19 M. A. Rego-Monteiro , E. M. F. Curado

We derive the global dynamic properties of the mMKG system (Maxwell coupled with a massive Klein-Gordon scalar field) with a general, unrestrictive class of data, in particular, for Maxwell field of arbitrary size, and by a gauge…

Analysis of PDEs · Mathematics 2019-02-26 Allen Fang , Qian Wang , Shiwu Yang

The Cauchy problem for the classical Dirac-Klein-Gordon system in two space dimensions is globally well-posed for L^2 Schoedinger data and wave data in H^{1/2} \times H^{-1/2}. In the case of smooth data there exists a global smooth…

Analysis of PDEs · Mathematics 2009-06-22 Axel Gruenrock , Hartmut Pecher

We study the Klein-Gordon-Zakharov system in two spatial dimensions, an important model in plasma physics. For small, smooth, and spatially localized initial data, we establish the global existence of solutions and characterize their sharp…

Analysis of PDEs · Mathematics 2025-09-04 Shijie Dong , Zihua Guo , Kuijie Li

The Cauchy problem for quadratic Klein-Gordon systems is considered in two spatial dimensions and higher under a suitable non-resonance condition on the masses, including the main case of equal masses. A global well-posedness and scattering…

Analysis of PDEs · Mathematics 2012-09-20 Tobias Schottdorf

We develop a trajectory construction of solutions to the massless wave equation in n+1 dimensions and hence show that the quantum state of a massive relativistic system in 3+1 dimensions may be represented by a stand-alone four-dimensional…

Quantum Physics · Physics 2019-09-06 Peter Holland

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations…

Analysis of PDEs · Mathematics 2012-08-14 Alexandru D. Ionescu , Benoit Pausader

This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…

Analysis of PDEs · Mathematics 2019-12-04 Pietro d'Avenia , Lorenzo Pisani , Gaetano Siciliano

In this article we will prove the global existence of a type of wave-Klein-Gordon system in $2+1$ spacetime dimension. Some technical tools such as conformal energy estimate on hyperboloid, normal form transform on Klein-Gordon equations…

Analysis of PDEs · Mathematics 2019-07-09 Yue Ma

Pointing out the difference between the Discrete Nonlinear Schr\"odinger equation with the classical power law nonlinearity-for which solutions exist globally, independently of the sign and the degree of the nonlinearity, the size of the…

Pattern Formation and Solitons · Physics 2007-05-23 Nikos I. Karachalios

We study the Dirac--Klein-Gordon system in $1+2$ spacetime dimensions. We show global existence of the solutions, as well as sharp time decay and linear scattering. One key advance is that we provide the first asymptotic stability result…

Analysis of PDEs · Mathematics 2023-11-15 Shijie Dong , Zoe Wyatt

In this work we consider the problem of global existence of small regular solutions to a type nonlinear wave-Klein-Gordon system with semi-linear interactions in two spatial dimension. We develop some new techniques on both wave equations…

Analysis of PDEs · Mathematics 2017-12-15 Yue MA

We consider an ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, which we call the relativistic Vlasov-Klein-Gordon system, we prove the existence of…

Analysis of PDEs · Mathematics 2009-11-07 Michael Kunzinger , Gerhard Rein , Roland Steinbauer , Gerald Teschl

The classical scalar massive field satisfying the Klein-Gordon equation in a finite one-dimensional space interval of periodically varying length with Dirichlet boundary conditions is studied. For the sufficiently small mass, the energy can…

Mathematical Physics · Physics 2008-11-26 J. Dittrich , P. Duclos

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 are interested in the stability of a class of totally geodesic wave maps, as recently studied by Abbrescia and Chen, and later by Duan and Ma. The relevant equations of motion are a system of coupled semilinear wave and Klein-Gordon…

Analysis of PDEs · Mathematics 2023-11-15 Shijie Dong , Zoe Wyatt

In this {\bf draft version} we prove inhomogeneous Strichartz estimates with spherical symmetry in the abstract setting via duality arguments. Then we derive some new explicit estimates in the context of the wave equation. This allows us to…

Analysis of PDEs · Mathematics 2009-04-01 Evgeni Y Ovcharov

We establish the global existence and scattering for small and localized solutions of the Klein-Gordon-Schr\"{o}dinger system in three dimensions. The system consists of coupled semilinear Schr\"{o}dinger and Klein-Gordon equations with…

Analysis of PDEs · Mathematics 2025-06-13 Chanjin You

We study the Klein-Gordon equation with general interaction term, which may be linear or nonlinear, and space-time dependent. The initial data is general, large and non-radial. We prove that global solutions are asymptotically given by a…

Analysis of PDEs · Mathematics 2023-04-11 Avy Soffer , Xiaoxu Wu