On the well-posedness for the generalized Ostrovsky, Stepanyarns and Tsimring equation

In this work we prove that the initial value problem associated with equation u(t) + u(xxx) - eta(Hu(x) + Hu(xxx)) + u(k)u(x) = 0, x is an element of R, t >= 0, where eta > 0 and H denotes the usual Hilbert transform, is locally well-posed in Sobolev spaces H-s (R) for s >= 0 and k = 1, 2, 3 and globally well-posed in L-2(R). (c) 2005 Elsevier Ltd. All rights reserved.6271277128