摘要

A nonlinear dispersive partial differential equation, which includes the famous Camassa-Holm and Degasperis-Procesi equations as special cases, is investigated. Although the H(1)-norm of the solutions to the nonlinear model does not remain constants, the existence of its weak solutions in lower order Sobolev space H(s) with 1 < s <= 3/2 is established under the assumptions u(0) epsilon H(s) and parallel to u(0x)parallel to(L)infinity < infinity. The local well-posedness of solutions for the equation in the Sobolev space H(s)(R) with s > 3/2 is also developed.