Asymptotics for the Korteweg-de Vries-Burgers equation

We study large time asymptotics of solutions to the Korteweg-de Vries-Burgers equation u(t) + uu(x) - u(xxx) = 0, x is an element of R, t > 0. We are interested in the large time asymptotics for the case when the initial data have an arbitrary size. We prove that if the initial data u(o) is an element of H(s) (R) boolean AND L(1) (R), where s > -1/2, then there exists a unique solution a (t, x) is an element of C(infinity) ((0, infinity); H(infinity) (R)) to the Cauchy problem for the Korteweg-de Vries-Burgers equation, which has asymptotics u (t) = t(-1/2) fM ((center dot)t(-1/2)) + o(t(-1/2)), where gamma is an element of (0, 1/2).