We consider Galerkin finite element methods for the nonlinear Klein-Gordon equation, giving the first optimal-order energy norm semidiscrete error estimates for non-Lipschitz nonlinearity. The result holds quite generally in one and two space dimensions and under a certain growth restriction in three. We also discuss some time stepping strategies and present numerical results.

The Einstein–Klein–Gordon field equations are solved in a inhomogeneous shear–free universe containing a material fluid, a self–interacting scalar field, a variable cosmological term, and a heat flux. A quintessence– dominated scenario arises with a power–law accelerated expansion compatible with the currently observed homogeneous universe.

We study the existence of vortices of the Klein-Gordon-Maxwell equations in the two dimensional case. In particular we find sufficient conditions for the existence of vortices in the magneto-static case, i.e when the electric potential φ = 0. This result, due to the lack of suitable embedding theorems for the vector potential A is achieved with the help of a penalization method.

Topological properties of the spaces of analytic test functions and distributions are investigated in the framework of the general theory of nonarchimedean locally convex spaces. The Laplace transform, topological isomorphism, is introduced and applied to the differential equations of nonarchimedean mathematical physics (Klein-Gordon and Dirac propagators).

We establish a local existence result for Dirac-Klein-Gordon equations in three space dimensions, employing a null form estimate and a fixed point argument. 0. Introduction and Main Results. In the present work, we like to study the Cauchy problem for the Dirac-Klein-Gordon equations. The unknown quantities are a spinor field ψ : R × R 7→ C and a scalar field φ : R × R 7→ R. The evolution equat...

We investigate the kink solutions to the generalized nonlinear Klein-Gordon equation in the presence of inhomogeneous forces and nonlocal operators. We have found that the number of kink internal modes can depend on the asymptotic behavior of the kink solution for large values of |x| . A list of mechanisms that are capable to create new kink internal modes would contain some of the following it...

We consider the Klein–Gordon equation associated with the Laplace– Beltrami operator ∆ on real hyperbolic spaces of dimension n≥2; as ∆ has a spectral gap, the wave equation is a particular case of our study. After a careful kernel analysis, we obtain dispersive and Strichartz estimates for a large family of admissible couples. As an application, we prove global well–posedness results for the c...

In this paper we consider the Klein—Gordon—Maxwell system in electrostatic case, assuming fall-off large-distance requirement on gauge potential. We are interested proving existence of finite energy (and charge) standing waves, having phase corresponding to mass coefficient Klein—Gordon Lagrangian.

and Applied Analysis 3 of φj (j = 0, 1, . . . , 5) to zero, we finally end up with a system of algebraic equations, namely,

A strict proof of equivalence between DuÆn-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic eld. First, Hamiltonian canonical approach to DKP theory is developed in matrix form. The theory is then quantized through the construction of the...