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Computation and Stability of Traveling Waves in Second Order Evolution Equations
SIAM Journal on Numerical Analysis
The topic of this paper are nonlinear traveling waves occuring in a system of damped waves equations in one space variable. We extend the freezing method from first to second order equations in time. When applied to a Cauchy problem, this method generates a comoving frame in which the solution becomes stationary. In addition it generates an algebraic variable which converges to the speed of the wave, provided the original wave satisfies certain spectral conditions and initial perturbations aredoi:10.1137/16m108286x fatcat:gs2qmj3dy5bhxn2lc4i5ypjzue