Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9501696 | Journal of Differential Equations | 2005 | 38 Pages |
Abstract
This paper presents an existence proof for symmetric modulating pulse solutions of a quasilinear wave equation. Modulating pulse solutions consist of a pulse-like envelope advancing in the laboratory frame and modulating an underlying wave train; they are also referred to as 'moving breathers' since they are time periodic in a moving frame of reference. The problem is formulated as an infinite-dimensional dynamical system with two stable, two unstable and infinitely many neutral directions. Using a partial normal form and a generalisation of local invariant-manifold theory to the quasilinear setting we prove the existence of modulating pulses on arbitrarily large, but finite domains in space and time.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Mark D. Groves, Guido Schneider,