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Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales
preprintposted on 2006-05-11, 10:02 authored by Mark D. Groves, G. Schneider
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 three stable, three unstable and infinitely many neutral directions. By transforming part of the equation into a normal form with an exponentially small remainder term and using a generalisation of local invariant-manifold theory to the quasilinear setting, we prove the existence of small-amplitude modulating pulses on domains in space whose length is exponentially large compared to the magnitude of the pulse.
- Mathematical Sciences
NotesThis is a pre-print.