Kazakopoulos Pavlos, Moustakas Aris L
Department of Physics, University of Athens, Athens 15784, Greece.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jul;78(1 Pt 2):016603. doi: 10.1103/PhysRevE.78.016603. Epub 2008 Jul 16.
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.
我们针对以高斯随机脉冲作为初始值函数的吸引性非线性薛定谔方程所对应的非厄米 Zakharov-Shabat 本征值问题计算李雅普诺夫指数。通过将 Thouless 公式扩展到非厄米随机算子，我们计算相应的态平均密度。我们还计算了决定本征函数渐近性的 Zakharov-Shabat 算子的一组散射数据的分布。我们分析了两种情况，一种是具有圆对称复高斯脉冲的情况，另一种是具有实高斯脉冲的情况。我们在通过非线性光纤进行信息传输的背景下讨论其意义。
