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Download fileModulating pulse solutions to quadratic quasilinear wave equations over exponentially long length scales
preprint
posted on 2006-05-11, 10:02 authored by Mark D. Groves, G. SchneiderModulating 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.
History
School
- Science
Department
- Mathematical Sciences
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430828 bytesPublication date
2006Notes
This is a pre-print.Language
- en