Perturbation of a shock wave

The Cauchy problem is considered for the perturbed Hopf equation u_t+uu_x=εf(u), ε→0. The solution in the continuity domain can be expanded in the standard asymptotic series in integral powers of the small parameter. An asymptotic representation is found for the line of propagation of the shock wave. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 118, No. 3, pp. 462–466, March, 1999.