PMID: 11308783Apr 20, 2001Paper

Soliton internal mode bifurcations: pure power law?

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
T KapitulaC K Jones

Abstract

The bifurcation of internal solitary wave modes from the essential spectrum has been one of the most exciting recent developments in the study of soliton dynamics. To date, it was believed that the bifurcation of such modes due to discretization has a strict power law dependence on the lattice discreteness parameter. In this work we prove that this dependence actually possesses relevant exponentially small terms which distinguish between different solutions for the discrete models. The theoretical result is established by using a discrete version of the Evans function. The predictions presented herein compare very favorably with the numerical study of the linear eigenvalue problem, and offer explanations of computational effects not possible on the basis of previous theoretical studies.

References

Nov 1, 1996·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·D HennigA Bülow
Feb 23, 1987·Physical Review Letters·H Segur, M D Kruskal
Oct 14, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·M Johansson, S Aubry

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Citations

Aug 11, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G Kevrekidis
Jul 24, 2014·Magnetic Resonance in Medicine : Official Journal of the Society of Magnetic Resonance in Medicine·Tammo RukatStefan A Reinsberg
May 15, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·P G KevrekidisE S Titi
Nov 3, 2001·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N R QuinteroF G Mertens

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