Moving kinks and nanopterons in the nonlinear Klein-Gordon lattice

A. V. Savin, Y. Zolotaryuk, J. C. Eilbeck

Research output: Contribution to journalArticle

Abstract

We study moving topological solitons (kinks and antikinks) in the nonlinear Klein-Gordon chain. These solitons are shown to exist with both monotonic (non-oscillating) and oscillating asymptotics (tails). Using the pseudo-spectral method, the (anti)kink solutions with oscillating background (so-called nanopterons) are found as travelling waves of permanent profile propagating with constant velocity. Each of these solutions may be considered as a bound state of an (anti)kink with a background nonlinear periodic wave, so that the wave "pushes" the (anti)kink over the Peierls-Nabarro barrier. The stability of these bound states is confirmed numerically. Travelling-wave solutions of permanent profile are shown to exist depending on the convexity of the on-site (substrate) potential. The set of velocities at which the (anti)kinks with monotonic asymptotics propagate freely is calculated. We also find moving non-oscillating (anti)kink profiles with higher topological charges, each of which appears to be the bound state of (anti)kinks with lower topological charge (\Q\ = 1). ©2000 Elsevier Science B.V. All rights reserved.

Original languageEnglish
Pages (from-to)267-281
Number of pages15
JournalPhysica D: Nonlinear Phenomena
Volume138
Issue number3-4
Publication statusPublished - 15 Apr 2000

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traveling waves
profiles
solitary waves
convexity
spectral methods

Keywords

  • Nanopterons
  • Nonlinear lattice
  • Pseudo-spectral method
  • Topological solitons

Cite this

Savin, A. V. ; Zolotaryuk, Y. ; Eilbeck, J. C. / Moving kinks and nanopterons in the nonlinear Klein-Gordon lattice. In: Physica D: Nonlinear Phenomena. 2000 ; Vol. 138, No. 3-4. pp. 267-281.
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Moving kinks and nanopterons in the nonlinear Klein-Gordon lattice. / Savin, A. V.; Zolotaryuk, Y.; Eilbeck, J. C.

In: Physica D: Nonlinear Phenomena, Vol. 138, No. 3-4, 15.04.2000, p. 267-281.

Research output: Contribution to journalArticle

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