Order parameter equations for front transitions: Nonuniformly curved fronts

Kinematic equations for the motion of slowly propagating, weakly curved fro nts in bistable media are derived. The equations generalize earlier derivat ions where algebraic relations between the normal front velocity and its cu rvature are assumed. Such relations do not capture the dynamics near nonequ ilibrium Ising-Bloch (NIB) bifurcations, where transitions between counterp ropagating Bloch fronts may spontaneously occur. The kinematic equations co nsist of coupled integro-diffential equations for the front curvature and t he front velocity, the order parameter associated with the NIB bifurcation. They capture the NIB bifurcation, the instabilities of Ising and Bloch fro nts to transverse perturbations, the core structure of a spiral wave, and t he dynamic process of spiral wave nucleation. Copyright (C) 1998 Published by Elsevier Science B.V.