We show asymptotic completeness for the charged Klein–Gordon equation in exterior De Sitter–Reissner–Nordström spacetime when product of charge black with Klein-Gordon field is small enough. then interpret scattering as transports along principal null geodesics a Kaluza–Klein extension original spacetime.

In this paper, new explicit wave solutions via liquid-gas bubbles are obtained for the fractional Kudryashov-Sinelshchikov (KS) equation under thermodynamic assumptions. A definition is applied to get these that utilized represent phenomenon of pressure waves conditions. Two analytical techniques used explore model which sinh-Gorden expansion and Riccati-Bernoulli Sub-ODE methods. These approac...

We show that every tempered distribution, which is a solution of the (homogenous) Klein-Gordon equation, admits a “tame” restriction to the characteristic (hyper)surface {x0 + x = 0} in (1 + n)-dimensional Minkowski space and is uniquely determined by this restriction. The restriction belongs to the space S′ ∂ − (R) which we have introduced in [16]. Moreover, we show that every element of S′ ∂ ...

In this paper we consider the nonexistence of global solutions of a Klein-Gordon equation of the form utt −∆u+mu = f(u), (t, x) ∈ [0, T )× Rn. Here m = 0 and the nonlinear power f(u) satisfies some assumptions which will be stated later. We give a sufficient condition on the initial datum with arbitrarily high initial energy such that the solution of the above Klein-Gordon equation blows up in ...

We consider positive, radial and exponentially decaying steady state solutions of the general reaction-diffusion and Klein-Gordon type equations and present an explicit construction of infinite-dimensional invariant manifolds in the vicinity of these solutions. The result is a precise stable manifold theorem for the reaction-diffusion equation and a precise center-stable manifold theorem for th...