Nonlinear solitary waves with Gaussian tails

We study analytically and numerically the stationary localized solutions of the nonlinear Schrodinger equation (NLSE) with an additional parabolic pot ential. Such a model occurs in a wide range of physical applications, inclu ding plasma physics and nonlinear optics. Bound states with Gaussian tails (these tails appear due to the parabolic linear potential) play an importan t role in the dynamics of the systems modelled by this equation. We prove t he existence of the bound states and describe their properties. (C) 1999 El sevier Science B.V. All rights reserved.