The change of signature of a metric is explained using simple examples and methods. The Klein-Gordon field on a signature-changing background is discussed, and it is shown how the approach of Dray et al. can be corrected to ensure that the KleinGordon equation holds. Isotropic cosmologies are discussed, and it is shown how the approach of Ellis et al. can be corrected to ensure that the Einstei...

We study travelling kinks in the spatial discretizations of the nonlinear Klein–Gordon equation, which include the discrete φ lattice and the discrete sine–Gordon lattice. The differential advance-delay equation for travelling kinks is reduced to the normal form, a scalar fourth-order differential equation, near the quadruple zero eigenvalue. We show numerically non-existence of monotonic kinks...

We study the scattering theory for the coupled KleinGordon-Schrödinger equation with the Yukawa type interaction in two space dimensions. The scattering problem for this equation belongs to the borderline between the short range case and the long range one. We show the existence of the wave operators to this equation without any size restriction on the Klein-Gordon component of the final state.

The formalism based on the equal-time Wigner function of the two-point correlation function for a quantized Klein–Gordon field is presented. The notion of the gauge-invariant Wigner transform is introduced and equations for the corresponding phase-space calculus are formulated. The equations of motion governing the Wigner function of the Klein–Gordon field are derived. It is shown that they lea...

An asymptotic nonlinear theory of the two superposed magnetic fluids is presented taking into account the spatial as well as temporal effects. A generalized formulation of the evolution equation governing the amplitude is developed which leads to the nonlinear Klein-Gordon equation. The various stability criteria are derived from this equation. Obtained also are the bell shaped soliton and the ...

We consider 2-D Klein Gordon equation with quadratic nonlinearity and prove Strichartz type dispersive estimates for the global solution with small initial data in the Sobolev space H.

We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.