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Computation and Stability of TravelingWaves in Second Order Evolution Equations

Beyn, Wolf-Jürgen; Otten, Denny; Rottmann-Matthes, Jens

Abstract: The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this method generates a comoving frame in which the solution becomes stationary. In addition it generates an algebraic variable which converges to the speed of the wave, provided the original wave satisfies certain spectral conditions and initial perturbations are sufficiently small. We develop a rigorous theory for this effect by recourse to some recent nonlinear stability results for waves in first order hyperbolic systems. Numerical computations illustrate the theory for examples of Nagumo and FitzHugh-Nagumo type.

Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht
Jahr 2016
Sprache Englisch
Identifikator DOI(KIT): 10.5445/IR/1000056075
ISSN: 2365-662X
URN: urn:nbn:de:swb:90-560758
KITopen ID: 1000056075
Verlag KIT, Karlsruhe
Umfang 33 S.
Serie CRC 1173 ; 2016/15
Schlagworte systems of damped wave equations, traveling waves, nonlinear stability, freezing method, second order evolution equations, point spectra and essential spectra
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