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 describes 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 data $(u_0,v_0)$ possesses certain regularity and sufficient decay as $|x|\to \infty ,$ then the solution $(u(t),v(t))$ will be smoother than $(u_0,v_0)$ for $0<t\le T$ where $T$ is the existence time of the solution.

arXiv admin note: text overlap with arXiv:nlin/0103012 by other authors

References in corpus (2)

• Finite time collapse of N classical fields described by coupled nonlinear Schrodinger equations
• Smoothing properties for the higher order nonlinear Schrödinger equation with constant coefficients