Well-posedness of Cauchy Problem for Coupled System of Long-short Wave Equations

Abstract

In this paper we study the Cauchy problem for a class of coupled equations which describe the resonant interaction between long wave and short wave. The global well-posedness of the problem is established in space H^{\frac{1}{2}+k} × H^k (k ∈ Z^+ ∪ {0}), the first and second components of which correspond to the short and long wave respectively.