HIGHER-ORDER NONLINEAR DISPERSIVE EQUATIONS

We study nonlinear dispersive equations of the form partial derivative (t)u + partial derivative(x)2j+1u + P(u, partial derivative(x)u, . . . , partial derivative(x)(2j)u) = 0, t is-an-element-of R, j is-an-elem ent-of Z+, where P(-) is a polynomial having no constant or linear ter ms. It is shown that the associated initial value problem is locally w ell posed in weighted Sobolev spaces. The method of proof combines sev eral sharp estimates for solutions of the associated linear problem an d a change of dependent variable which allows us to consider data of a rbitrary size.