EXISTENCE AND UNIQUENESS RESULTS FOR A SYSTEM OF COUPLED KDV EQUATIONS IN WEIGHTED SOBOLEV SPACE

Abstract

The system of Korteweg–De Vries (KdV) equations is a system of partial differential equations. It is used to describe the modeling of shallow water surface waves. In this paper, we show the well-posedness of the coupled Korteweg–De Vries system of equations with initial data under Sobolev Space and Weighted Sobolev Space for 3/4 ≤ s ≤ 1.