Existence of travelling wave front solutions of a two-dimensional anisotropic model

This paper considers a two-dimensional anisotropic [email protected]"[email protected]"0^[email protected]+k"0^2^[email protected]@?k"0^[email protected]?"y^[email protected][email protected]"0^[email protected]?"x^[email protected]?"y^[email protected]@j^3,introduced by Pesch and Kramer (1986) [28]. Assume that @j travels with a speed c in the propagation direction x and is periodic in the transverse direction y. This model is formulated as a spatial dynamic system in which the variable x is a time-like variable. A center-manifold reduction technique and a normal form analysis are applied to show that this dynamic system can be reduced to a system of ordinary differential equations. A bifurcation analysis yields the persistence of the heteroclinic orbit for the reduced system when higher order terms are added and the speed c is small enough, which establishes the existence of travelling wave front solutions. In order to overcome the difficulty caused by the irreversibility, some appropriate constants are adjusted.

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