Instability of local deformations of an elastic rod: Numerical evaluation of the evans function

We present a method for the numerical evaluation of the Evans function that doesnot require integration in an associated exterior algebra space. This technique is suitable for thedetection of bifurcations and is particularly useful when the dimension of the linearized systemand/or the dimension of the converging subspaces at infinity is large. We test this approach byinvestigating the stability of a two-parameter family of traveling pulse solutions to two coupledKlein-Gordon equations. The spectral stability of these pulses is completely understood analytically [S. Lafortune and J. Lega, SIAM J. Math. Anal. , 36 (2005), pp. 1726-1741], and we show that ournumerical method is able to detect bifurcations of the pulse family with very good accuracy.