具有周期势的非线性薛定谔方程中调制脉冲的相互作用
Interaction of modulated pulses in the nonlinear Schroedinger equation with periodic potential
摘要：
考虑一类具有周期位势的三次非线性Schroedinger方程.在半经典标度下，研究了集中在一个或几个布洛赫带内的调制脉冲的非线性相互作用。封闭模式系统的概念被引入，它允许严格推导的振幅方程描述这些脉冲的宏观动力学的有限系统。
英文摘要：
We consider a cubic nonlinear Schroedinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic dynamics of these pulses.
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