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Modulating pulse solutions for quasilinear wave equations
preprint
posted on 2005-08-16, 14:14 authored by Mark D. Groves, G. SchneiderThis 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.
History
School
- Science
Department
- Mathematical Sciences
Pages
252565 bytesPublication date
2005Notes
This is a pre-print.Language
- en