Spatial analyticity of solutions for a coupled system of generalized KdV equations

Abstract

We consider the well‐posedness of a coupled system for generalized Korteweg–de Vries (S‐gKdV) where and the initial data are analytic in a strip and then the solutions of S‐gKdV continue to be analytic in a strip the width of which will decrease as time goes to , by using the standard contraction method in analytic Bourgain space. Besides, we obtain algebraic lower bounds on the decreasing rate of the uniform radius of analyticity of the solutions.