Step-like contrast structure for a quasilinear system of singularly perturbed differential equations with a zero characteristic number

We consider a system of singularly perturbed first-order differential equations with a zero characteristic number. The solution of such a problem is characterized by the presence of a contrast structure, that is, of an internal transition layer on a given interval. We prove the existence of an exact solution with a step-like contrast structure and construct its uniform asymptotic expansion. An example is given.