Novel Lower Bounds on the Radius of Spatial Analyticity for the KdV Type Equations

In this article, using multi-linear estimate in Bourgain type spaces, we prove the local well-posedness of initial value problem associated with the equation partial derivative(w)(t)+partial derivative(3)(x)w+eta(t)Lw+partial derivative(x)(w)(k)=0,k=2,4. The solution is established on the line for analytic initial data u 0 that can be extended as holomorphic functions in a strip around the x-axis. A procedure for constructing a global solution is proposed, which improve earlier results in [1].