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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/1684

Title: Modulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales
Authors: Groves, Mark D.
Schneider, G.
Keywords: quasilinear wave equations,
spatial dynamics
moving breathers
Issue Date: 2006
Abstract: 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.
Description: This is a pre-print.
URI: https://dspace.lboro.ac.uk/2134/1684
Appears in Collections:Pre-prints (Maths)

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