Local well-posedness of the initial value problem for a fourth-order nonlinear dispersive system on the real line

Abstract

This paper investigates the initial value problem for a system of one-dimensional fourth-order dispersive partial differential-integral equations with nonlinearity involving derivatives up to second order. Examples of the system arise in relation with nonlinear science and geometric analysis. Applying the energy method based on the idea of a gauge transformation and Bona-Smith approximation technique, we prove that the initial value problem is time-locally well-posed on the real line for initial data in a Sobolev space with high regularity.