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.