Local well-posedness of a nonlinear KdV-type equation (Q392611)

In this paper, the Cauchy problem for a generalized nonlinear KdV-type equation with time- and space-dependent coefficients is considered. The authors prove the local well-posedness of the initial value problem by a standard Picard iterative scheme under a condition of non-degeneracy of a dispersive coefficient. The authors show that the control of the dispersive and diffusion terms is possible if an adequate weight function determined with respect to the dispersive and diffusion coefficients is used to define energy. The dispersive properties of the equation are used to prove the existence and uniqueness of solutions.