STEADY-STATE PLANE-WAVE PROPAGATION SPEED IN EXCITABLE MEDIA

With the view to excitation waves in neuromuscular tissue we study the propagation speed c of steady state plane trigger waves as a function of the shape parameters of the nonlinear source function in the react ion diffusion equation (the slow recovery variable is assumed frozen). The nonlinear eigenvalue problem, which yields c as the eigenvalue an d the wave profile u(xi) as the eigenfunction, is reformulated to allo w us to construct a variety of exactly solvable models, in particular the waves with profiles having central symmetry about their midpoints. Trigger waves with asymmetric profiles are also considered. The propa gation speed c is expressed in terms of the shape parameters of the no nlinear source function i(u). We show that among shape parameters of i (u) there are only three essential ones which control the propagation speed. We derive a general expression for the propagation speed, which has the same simple form as in the well known case with the sawtoothw ise i(El) but with one parameter appropriately redefined. We also intr oduce a simple iterative procedure for solving the nonlinear eigenvalu e problem. Finally introducing a new exactly solvable model we show th at the effect of noninstantaneous activation on the propagation speed can be reduced to renormalization of one of the steady state model's p arameter.