Periodic wave shock solutions of Burgers equations

In this paper, we present an new approach for the study of Burgers equations. Our purpose is to describe the asymptotic behavior of the solution in the cauchy problem for viscid equation with small parameter $ {\varepsilon } $ and to discuss in particular the case of periodic wave shock. We show that the solution of this problem approaches the shock-type solution for the cauchy problem of the inviscid burgers equation. The results are formulated in classical mathematics and proved with infinitesimal techniques of nonstandard analysis