Well-posedness of the cauchy problem for the coupled system of the Schrödinger-KdV equations

This paper is devoted to the study of the Cauchy problem for the coupled system of the Schrödinger-KdV equations which describes the nonlinear dynamics of the one-dimensional Langmuir and ion-acoustic waves. Global well-posedness of the problem is established in the spaceH . .H . (. .Z +), the first and second components of which correspond to the electric field of the Langmuir oscillations and the low-frequency density perturbation respectively.