On the solitary solutions for the nonlinear Klein-Gordon equation coupled with Born-Infeld theory

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Analytical solutions for the fractional Klein-Gordon equation

In this paper, we solve a inhomogeneous fractional Klein-Gordon equation by the method of separating variables. We apply the method for three boundary conditions, contain Dirichlet, Neumann, and Robin boundary conditions, and solve some examples to illustrate the effectiveness of the method.

Coupled Klein–Gordon and Born–Infeld type equations: looking for solitary waves

where u is a real function and ω ∈ R. If one looks for solutions of (1.1) having the form (1.2), the nonlinear Klein-Gordon equation reduces to a semilinear elliptic equation, as well as if one looks for solitary waves of nonlinear Schrödinger equation (see [10], [12] and the papers quoted therein). Many existence results have been established for solutions u of such a semilinear equation, both...

Multi-solitary waves for the nonlinear Klein-Gordon equation

We consider the nonlinear Klein-Gordon equation in R. We call multi-solitary waves a solution behaving at large time as a sum of boosted standing waves. Our main result is the existence of such multi-solitary waves, provided the composing boosted standing waves are stable. It is obtained by solving the equation backward in time around a sequence of approximate multisolitary waves and showing co...

On Global Attraction to Solitary Waves for the Klein-Gordon Equation Coupled to Nonlinear Oscillator

The long-time asymptotics is analyzed for all finite energy solutions to a model U(1)invariant nonlinear Klein-Gordon equation in one dimension, with the nonlinearity concentrated at a point. Our main result is that each finite energy solution converges as t→ ±∞ to the set of “nonlinear eigenfunctions” ψ(x)e−iωt. Résumé. Attraction Globale vers des Ondes Solitaires pour l’Équation de KleinGordo...