ANALYSIS OF A SINGULARLY PERTURBED TRAVELING-WAVE PROBLEM

A singularly perturbed traveling wave problem derived from the drift d iffusion model describing electron transport in two-valley semiconduct or materials is analysed. It is shown that the reduced problem, define d on a submanifold of the phase space, has homoclinic orbits for certa in parameters. By using methods from invariant manifold theory and met hods from homoclinic continuation theory, it is proved that the homocl inic orbits of the reduced problem persist in a global center manifold near the manifold of the reduced problem.