On the Cauchy Problem for a K.P.-Boussinesq-Type System

In this work, we prove that the Cauchy problem is locally well-posed for all μ and ν 0 in the anisotropic Sobolev space Ys, s>2. For ν>0, we establish global well-posedness for small data. We also show the existence of solitary-wave solutions for this system and prove regularity and analyticity of this kind of solutions.