Travelling waves in lattice models of multi-dimensional and multi-component media. I. General hyperbolic properties
- 1 May 1993
- journal article
- Published by IOP Publishing in Nonlinearity
- Vol. 6 (3) , 429-455
- https://doi.org/10.1088/0951-7715/6/3/006
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 prime 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.Keywords
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