Homoclinic Structure of Zakharov Equations


Emily M. Tian

Wright State University




Using perturbation theory, we get a low dimensional representation for the one-soliton case for Zakharov equations, subject to periodic boundary conditions and a symmetry constraint. This low dimensional representation is a dynamical equation having one degree of freedom. We present a quantitative description of the stable one spatial dimensional homoclinic structure, which is responsible for the onset of stochastic motion in higher dimensions. Some features of Zakharov equations are also discussed based on the low dimensional representation.