Near-Integrability of Periodic Klein-Gordon Lattices

Integrability of Klein - Gordon Equations *

Usin the Painlev test, it is shown that the only interablc nonlinear Klein-Gordon equations ux,=f(u) with f a linear combination of exponentials are the Liouville, sine-Gordon (or sinh-Gordon) and Mikhailov equations. In particular, the double sine-Gordon equation is not interable.

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

— 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...

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...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION

Exact discrete breather compactons in nonlinear Klein-Gordon lattices.

We demonstrate the existence of exact discrete compact breather solutions in nonlinear Klein-Gordon systems, and complete the work of Tchofo Dinda and Remoissenet [Phys. Rev. E 60, 6218 (1999)], by showing that the breathers stability is related principally to the lattice boundary conditions, the coupling term, and the harmonicity parameter.