title: Nonlinear Schrödinger equation with random Gaussian input: distribution of inverse scattering data and eigenvalues.
abstract: We calculate the Lyapunov exponent for the non-Hermitian Zakharov-Shabat eigenvalue problem corresponding to the attractive nonlinear Schrödinger equation with a Gaussian random pulse as an initial value function. Using an extension of the Thouless formula to non-Hermitian random operators, we calculate the corresponding average density of states. We also calculate the distribution of a set of scattering data of the Zakharov-Shabat operator that determine the asymptotics of the eigenfunctions. We analyze two cases, one with circularly symmetric complex Gaussian pulses and the other with real Gaussian pulses. We discuss the implications in the context of information transmission through nonlinear optical fibers.
authors.affiliation: Department of Physics, University of Athens, Athens 15784, Greece.
authors.forename: Pavlos
authors.initials: P
authors.lastname: Kazakopoulos
authors.forename: Aris L
authors.initials: AL
authors.lastname: Moustakas