Existence and stability of accelerating solitons in sliding-frequency filter systems.

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.