Phys. Rev. E 71, 066611 (2005) [9 pages]Existence and stability of accelerating solitons in sliding-frequency filter systemsReceived 27 January 2005; published 28 June 2005 Sliding-frequency filter systems are known to admit two families of accelerating solitons: high-amplitude and low-amplitude families. Such equilibrium solutions are computed here, for a wide range of filter strengths, as self-similar solutions having Airy function asymptotics. In a limited parameter region, the profile possesses a secondary small hump. The high-amplitude solitons are found to be stable over a region of parameter space which is here determined by the Evans function method, adjusted to Airy function asymptotics. The loss of stability is due to a Hopf bifurcation. © 2005 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevE.71.066611
DOI:
10.1103/PhysRevE.71.066611
PACS:
42.65.Tg, 42.65.Sf, 42.81.Dp
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