Modulating pulse solutions for quasilinear wave equations |
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Authors: | Mark D. Groves Guido Schneider |
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Affiliation: | a Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK b Mathematisches Institut I, Universität Karlsruhe, 76128 Karlsruhe, Germany |
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Abstract: | 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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Keywords: | 35L05 37G05 37K50 |
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