Novel Lower Bounds on the Radius of Spatial Analyticity for the KdV Type Equations - Boukarou, Aissa; Guerbati, Kaddour; Zennir, Khaled; Mansouri, Aouatef (Journal of Applied Nonlinear Dynamics, 2026)
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 _tw +_x^3w +η(t) Lw+_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].