Trapping of kinks and solitons by defects: phase space transport in finite-dimensional models
Philip Holmes, Roy Goodman, and Michael Weinstein. Progress in Nonlinear Science, Vol. 1 (Nizhny Novgorod, 2001), 2002.
Jan 1, 2002·
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0 min read
Philip Holmes
Roy Goodman
Michael Weinstein
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.
Type
Publication
Progress in Nonlinear Science, Vol. 1 (Nizhny Novgorod, 2001), 103–115
Authors
Professor, Associate Chair for Graduate Studies, Department of Mathematical Sciences
I am a professor in the Department of Mathematical Sciences at NJIT. My research applies methods of dynamical systems to (conservative, dispersive) nonlinear wave equations arising, for example, in optics and fluid mechanics. I am interested in dynamical and bifurcation phenomena, and I use techniques from Hamiltonian mechanics and perturbation theory, as well as extensive computations. My current research in vortex dynamics is supported by the NSF under DMS-2206016.
I led the effort to start the SIAM New York-New Jersey-Pennsylvania Section (SIAM NNP) and was its first president in 2023-2024. I have handed over the reins to a new leadership group.
