Trapping of kinks and solitons by defects: phase space transport in finite-dimensional models

Abstract

We study models of Fei et al. and of Forinash et al of kinks in the sine-Gordon equation, and solitons in the nonlinear Schrodinger equation interacting with point defects. The models are two and three degree-of-freedom Hamiltonian systems. Using dynamical systems methods, we show that they exhibit interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics and complex and delicate structures describing the interaction of traveling waves with the defect. We interpret the behavior in terms of invariant manifolds and phase space transport theory.

Philip Holmes

Professor Emeritus

Roy Goodman

Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences

My research interests include dynamical systems and nonlinear waves, vortex dynamics, quantum graphs, and network inference

Michael Weinstein

Professor