STABILITY OF LARGE PERIODIC SOLUTIONS OF KLEIN-GORDON NEAR A HOMOCLINIC ORBIT by

Stability of Large Periodic Solutions of Klein-Gordon Near a Homoclinic Orbit

— We consider the Klein-Gordon equation (KG) on a Riemannian surface M ∂ t u−∆u−mu+ u = 0, p ∈ N, (t, x) ∈ R×M, which is globally well-posed in the energy space. Viewed as a first order Hamiltonian system in the variables (u, v ≡ ∂tu), the associated flow lets invariant the two dimensional space of (u, v) independent of x. It turns out that in this invariant space, there is a homoclinic orbit t...

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.

Bifurcations and Stability of Nondegenerated Homoclinic Loops for Higher Dimensional Systems

By using the foundational solutions of the linear variational equation of the unperturbed system along the homoclinic orbit as the local current coordinates system of the system in the small neighborhood of the homoclinic orbit, we discuss the bifurcation problems of nondegenerated homoclinic loops. Under the nonresonant condition, existence, uniqueness, and incoexistence of 1-homoclinic loop a...

Travelling breathers in Klein-Gordon lattices as homoclinic orbits to p−tori

Klein-Gordon chains are one-dimensional lattices of nonlinear oscillators in an anharmonic on-site potential, linearly coupled with their first neighbours. In this paper, we study the existence in such networks of spatially localized solutions, which appear time periodic in a referential in translation at constant velocity. These solutions are called travelling breathers. In the case of travell...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION