The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that correspond to cosmologies. These spacetimes are studied here, and include among them a solution exhibiting both early inflation and later continued rapid expansion ...

We prove sharp Morawetz estimates – global in time with a singular weight in the spatial variables – for the linear wave, Klein–Gordon and Schrödinger equations, for which we can characterise the maximisers. We also prove refined inequalities with respect to the angular integrability.

We study the existence of cylindrically symmetric electro-magnetostatic solitary waves for a system of a nonlinear Klein–Gordon equation coupled with Maxwell’s equations in presence of a positive mass and of a nonnegative nonlinear potential. Nonexistence results are provided as well.

In this paper we present numerical solutions by the fourth order implicit finite difference scheme to nonlinear Klein-Gordon-Schrödinger equations with a perturbed term. We discuss the accuracy and stability of the scheme. Numerical tests are used to assess the performance of the scheme.

It is proved that no Hamiltonian exists for the real Klein-Gordon field used in the Yukawa interaction. It is also shown that a real Klein-Gordon particle can be neither in a free isolated state nor in a bound state having an angular momentum l > 0. The experimental data support these conclusions. This outcome is in a complete agreement with Dirac's negative opinion on the Klein-Gordon equation.

Some new generalized solitary solutions of the Klein–Gordon–Schrödinger equations are obtained using the Exp-function method, which include some known solutions obtained by the F-expansion method and the homogeneous balance method in the open literature as special cases. It is shown that the Exp-function method is a straight, concise, reliable and promising mathematical tool for solving nonline...

Abstract. The Levi-Civita transformation is applied in the two-dimensional (2D) Dirac and Klein-Gordon (KG) equations with equal external scalar and vector potentials. The Coulomb and harmonic oscillator problems are connected via the LeviCivita transformation. These connections lead to an approach to solve the Coulomb problems using the results of the harmonic oscillator potential in the above...

In this paper we construct a parametrix for the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces without caustics. We use this parametrix to obtain asymptotic expansions for solutions of ( − λ)u = f and to obtain a uniform L estimate for a family of bump functions traveling to infinity.

We give a brief survey of applications of the Gearhart-Prüss spectral mapping theorem for abstract strongly continuous semigroups on Hilbert spaces to the study of stability of solitary waves for a large class of Hamiltonian partial differential equations of mathematical physics including Klein-Gordon, nonlinear Schrödinger, Boussinesq, Benjamin-BonaMahoney (regularized long-wave), Korteweg-deV...

In this report, we study various nonlinear wave equations arising in mathematical physics and investigate the existence of solutions to these equations using variational methods. In particular, we look for particle-like traveling wave solutions known as solitary waves. This study is motivated by the prevalence of solitary waves in applications and the rich mathematical structure of the nonlinea...