We study the asymptotic behavior in time of the solutions of a system of nonlinear Klein-Gordon equations. We have two basic results: First, in the L@R3) norm, solutions decay like 0(t-3/2) as t/+ provided the initial data are sufficiently small. Finally we prove that finite energy solutions of such a system decay in local energy norm as t++.

The aim of this present work is to study the blow-up dynamics and lifespanestimate for solution higher dimensional Klein-Gordon Equation in subcritical case, which1 < p psc. We construct equation motion from Lagrangian withnon-minimal coupling, where coupling interaction scalar field proportional thescalar curvature spacetime. has form like nonlinear dampedwave with mass. novelty time depend...

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 the quantum hyperbolic equation formulated in [1] is applied to the study of the propagation of the initial thermal state of the Universe. It is shown that the propagation depends on the barrier height. The Planck wall potential is introduced, VP = h̄/8tP = 1.25 10 GeV where tP is a Planck time. For the barrier height V < VP the master thermal equation is the modified Klein-Gordon ...

In this paper, a new auxiliary equation method is proposed. Combined with the mapping method, abundant periodic wave solutions for generalized Klein-Gordon and Benjamin are obtained. They types of which rarely found in previous studies. As m → 0 1, some trigonometric solitary also obtained correspondingly. This promising constructing nonlinear evolution equations (NLEEs) mathematical physics.

The semilinear Klein-Gordon equation with initial conditions is studied in de Sitter spacetime. L? decay estimates are derived for the solutions to linear Klein- Gordon equations and without source term It also showed global existence of value problem power type non-linear terms small data by using these

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...

An useful strategy for the study of nonlinear partial differential equations (PDE) arising in pattern formation is to consider asymptotic solutions containing one or several localized defects and to simplify the dynamics by finding the equations of motion of the system of interacting defects. The great advantage of this approach is that we are dealing with ordinary differential equations (ODEs)...

Abstract. We are interested in the problem of existence of soliton-like solutions for the nonlinear Klein-Gordon equation. In particular we study some necessary and sufficient conditions on the nonlinear term to obtain solitons of a given charge. We remark that the conditions we consider can be easily verified. Moreover we show that multiplicity of solitons of the same charge is guaranteed by t...