Gain of regularity for a coupled system of generalized nonlinear Schrödinger equations

Abstract

In this paper, we study the smoothness properties of solutions to a one‐dimensional coupled nonlinear Schrödinger system equations that describe some physical phenomena such as propagation of polarized laser beams in birefringent Kerr medium in nonlinear optics. We show that the equations dispersive nature leads to a gain in regularity for the solution. In particular, if the initial datum possesses certain regularity and sufficient decay as , then the solution will be smoother than for , where is the existence time of the solution.