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Modulating pulse solutions for quasilinear wave equations

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posted on 16.08.2005 by Mark D. Groves, G. Schneider
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.

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252565 bytes

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2005

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