Type: Article

Asymptotics of solutions to the generalized Ostrovsky equation

Hayashi, Nakao; Naumkin, Pavel I.; Niizato, Tomoyuki;

Abstract:

We consider the Cauchy problem for the generalized Ostrovsky equation u(tx) = u + (f(u))xx, where f(u) = vertical bar u vertical bar(rho-1)u if rho is not an integer and f(u) = u(rho) if rho is an integer. We obtain the L-infinity time decay estimates and the large time asymptotics of small solutions under suitable conditions on the initial data and the order of the nonlinearity. (C) 2013 Elsevier Inc. All rights reserved.