Dept. of Phys., Penn State Univ., University Park, PA 16802
It is now well known that disorder in one-dimensional systems results in normal modes that are exponentially localized (Anderson localization). The propagation of waves and pulses through a disordered system is dramatically affected by the localization, and there is some interesting exceptional behavior. The problem is made further interesting by the addition of nonlinearity. A basic question is whether or not nonlinearity destroys Anderson localization. Of all the references, half predict that localization is destroyed, and half predict that it is not. Continuous wave and pulse experiments have been performed on nonlinear disordered acoustic systems and some interesting results have been obtained. An analysis of a nonlinear periodic system, which shows effects of basin crowding, will also be presented. [Work supported by NSF DMR 9000549 and ONR.] P. Devillard and B. Souillard, J. Stat. Phys. (1986); B. Doucot and R. Rammal, Europhys. Lett. (1987); C. Albanese and J. Frohlich, Commun. Math. Phys. (1988); Q. Li et al., Phys. Rev. B (1988); A. Soffer and M. I. Weinstein, Commun. Math. Phys.; R. Bourbonnais and R. Maynard, Phys. Rev. Lett. (1990); Yu. S. Kivshar et al. (1990); R. Knapp et al., Disorder and Nonlinearity, edited by A. R. Bishop, D. K. Campbell, and S. Pnevmatikos (1989).