### ASA 125th Meeting Ottawa 1993 May

## 2pPA5. Pulses, nonlinearity, and Anderson localization.

**J. D.Maynard
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*Dept. of Phys., Penn State Univ., University Park, PA 16802
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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,[1] 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).