DYNAMICS OF KLEIN-GORDON ON A COMPACT SURFACE NEAR A HOMOCLINIC ORBIT

作者：Grebert Benoit^*; Jezequel Tiphaine; Thomann Laurent

来源：Discrete and Continuous Dynamical Systems, 2014, 34(9): 3485-3510.

DOI：10.3934/dcds.2014.31.3485

• Klein-Gordon equation
• wave equation
• homoclinic orbit
• center manifold

We consider the Klein-Gordon equation (KG) on a Riemannian surface M %26lt;br%26gt;partial derivative(2)(t) - Delta u - m(2)u + u(2p+1) = 0, p is an element of N*, (t,x) is an element of R x M, %26lt;br%26gt;which is globally well-posed in the energy space. This equation has a homoclinic orbit to the origin, and in this paper we study the dynamics close to it. Using a strategy from Groves-Schneider, we get the existence of a large family of heteroclinic connections to the center manifold that are close to the homoclinic orbit during all times. We point out that the solutions we construct are not small.

• 出版日期2014-9
• 单位INRIA