Travelling waves in lattice models of multi-dimensional and multi-component media. I. General hyperbolic properties

V. Afraimovich, Ya Pesin

Research output: Contribution to journalArticle

33 Scopus citations

Abstract

The authors study the stability of motion in the form of travelling waves in lattice models of unbounded multi-dimensional and multi-component media with a nonlinear ′ term and small coupling depending on a finite number of space coordinates. Under certain conditions on the nonlinear term we show that the set of travelling waves running with the same sufficiently large velocity forms a finite-dimensional submanifold in infinite-dimensional phase space endowed with a special metric with weights. It is 'almost' stable and contains a finite-dimensional strongly hyperbolic subset invariant under both evolution operator and space translations.

Original languageEnglish (US)
Article number006
Pages (from-to)429-455
Number of pages27
JournalNonlinearity
Volume6
Issue number3
DOIs
StatePublished - Dec 1 1993

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)
  • Applied Mathematics

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