Decomposition of Traveling Wave Existence Problem for Singularly Perturbed Equations

The studies of the phenomena of transient traveling waves on transmission lines are interesting in the theoretical phase simulations and real applications. The traveling waves problem for the singularly perturbed semi-linear parabolic equations is considered in the paper. It is shown that the corresponding problem for a singularly perturbed ODE system can be reduced to a certain problem of lower dimension using a splitting transformation based on the technique of slow and fast integral manifolds.