%0 Unpublished Work %A Groves, Mark D. %A Schneider, G. %D 2005 %T Modulating pulse solutions for quasilinear wave equations %U https://repository.lboro.ac.uk/articles/preprint/Modulating_pulse_solutions_for_quasilinear_wave_equations/9380285 %2 https://repository.lboro.ac.uk/ndownloader/files/16991828 %K untagged %K Mathematical Sciences not elsewhere classified %X 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. %I Loughborough University