Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model

Roy H. Goodman; Philip J. Holmes; Michael I. Weinstein

doi:10.1016/S0167-2789(01)00353-0

Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model

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

Research output: Contribution to journal › Article › peer-review

53 Scopus citations

Abstract

We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.

Original language	English (US)
Pages (from-to)	21-44
Number of pages	24
Journal	Physica D: Nonlinear Phenomena
Volume	161
Issue number	1-2
DOIs	https://doi.org/10.1016/S0167-2789(01)00353-0
State	Published - Jan 1 2002
Externally published	Yes

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Hamiltonian systems
Homoclinic orbits
Nonlinear waves
Phase space transport
Radiation damping
Two-mode model

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10.1016/S0167-2789(01)00353-0

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@article{f31a9c1ea7794f3294381277bf756928,

title = "Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model",

abstract = "We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.",

keywords = "Hamiltonian systems, Homoclinic orbits, Nonlinear waves, Phase space transport, Radiation damping, Two-mode model",

author = "Goodman, {Roy H.} and Holmes, {Philip J.} and Weinstein, {Michael I.}",

note = "Funding Information: RG was supported by NSF DMS-9901897and Bell Laboratories—Lucent Technologies under the Post-doctoral Fellowship with Industry Program. PH was partially supported by DoE: DE-FG02-95ER25238. We thank Florin Diacu for drawing our attention to Littlewood{\textquoteright}s paper, and our editor Chris Jones and one of the referees for pointing out the work of Birnir and Campbell et al. ",

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doi = "10.1016/S0167-2789(01)00353-0",

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volume = "161",

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TY - JOUR

T1 - Interaction of sine-Gordon kinks with defects

T2 - Phase space transport in a two-mode model

AU - Goodman, Roy H.

AU - Holmes, Philip J.

AU - Weinstein, Michael I.

N1 - Funding Information: RG was supported by NSF DMS-9901897and Bell Laboratories—Lucent Technologies under the Post-doctoral Fellowship with Industry Program. PH was partially supported by DoE: DE-FG02-95ER25238. We thank Florin Diacu for drawing our attention to Littlewood’s paper, and our editor Chris Jones and one of the referees for pointing out the work of Birnir and Campbell et al.

PY - 2002/1/1

Y1 - 2002/1/1

N2 - We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.

AB - We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.

KW - Hamiltonian systems

KW - Homoclinic orbits

KW - Nonlinear waves

KW - Phase space transport

KW - Radiation damping

KW - Two-mode model

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U2 - 10.1016/S0167-2789(01)00353-0

DO - 10.1016/S0167-2789(01)00353-0

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SN - 0167-2789

VL - 161

SP - 21

EP - 44

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 1-2

ER -

Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model

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All Science Journal Classification (ASJC) codes

Keywords

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