Strong NLS Soliton-Defect Interactions

By Roy H. Goodman, Philip J. Holmes, Michael I. Weinstein. 2002

219 citations recorded by the source corpus.

We consider the interaction of a nonlinear Schrodinger soliton with a spatially localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected, transmitted, or captured by the defect. We propose a mechanism of resonant energy transfer to a nonlinear standing wave mode supported by the defect. Extending Forinash et al. [Phys. Rev. E 49 (1994) 3400], we then derive a finite-dimensional model for the interaction of the soliton with the defect via a collective coordinates method. The resulting system is a three degree-of-freedom Hamiltonian with an additional conserved quantity. We study this system both numerically and using the tools of dynamical systems theory, and find that it exhibits a variety of interesting behaviors, largely determined by the structures of stable and unstable manifolds of special classes of periodic orbits. We use this geometrical understanding to interpret the simulations of the finite-dimensional model, compare them with the nonlinear Schrodinger simulations, and comment on differences due to the finite-dimensional ansatz.

Subfields: Computer Networks and Communications, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/bf5bc02911beacb0323c32e05d7d3ffd0d76b118

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Selection of the ground state for nonlinear schrödinger equations (2003, background): “ has been shown that equations of this type arise as the equation governing the evolution of the envelope of the electric ﬁeld of a light pulse propagating in a medium with defects. See, for example, [17, 18, 19]. 10 Acknowledgments: This work was supported in part by grants from the National Scienc”
Fast Soliton Scattering by Delta Impurities (2006, background): “Scattering of solitons by delta impurities is a natural model explored extensively in the physics literature – see for instance [2],[8], and references given there.”