Transverse wall instabilities on a driven, damped two-dimensional lattice system

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Abstract
Analytic and numerical studies are presented for the onset and saturation of transverse patterns occurring on walls propagating in a two-dimensional, longitudinally discrete, underdamped, dc-driven Frenkel-Kontorova model. For sufficiently weak damping, transverse instabilities occur at a series of critical field thresholds, where the wall velocity is of intermediate magnitude. Typically, the transverse patterns saturate as counterpropagating kink-antikink pairs, whose nucleation supports the longitudinal wall propagation. The wall dynamics in a D-dimensional lattice is governed approximately by a damped drive (D-1)-dimensional sine-Gordon equation.