Traveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials
Traveling Solitary Waves in the Periodic Nonlinear Schrödinger Equation with Finite Band Potentials
复制标题
具有有限带势的周期性非线性薛定谔方程中的行孤立波
DOI：
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发表时间：
2013
影响因子：
1.9
通讯作者：
T. Dohnal
中科院分区：
文献类型：
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作者：
T. Dohnal
本文研究了一维周期非线性薛定谔方程（PNLS）中有限对比度非线性周期结构（"深光栅“）中运动间隙孤子的渐近性。由有限带势描述的周期性结构在线性带结构中的带函数的横向交叉和对势的周期性扰动产生新的小间隙。在这些带隙中，尽管存在深光栅，但仍存在速度为O（1）的新型带隙孤子。利用满足广义耦合模方程组（gCME）的慢变包络和交叉点处的布洛赫波，给出了间隙孤子的近似解。交叉点处的本征空间是二维的，必须选择属于两个带函数的布洛赫波。这是通过优化算法实现的。的gCME的行波孤波解，然后导致近孤波解的PNLS移动在一个$O（1）$的速度通过周期性结构…
This paper studies asymptotics of moving gap solitons in nonlinear periodic structures of finite contrast (``deep grating'') within the one dimensional periodic nonlinear Schrodinger equation (PNLS). Periodic structures described by a finite band potential feature transversal crossings of band functions in the linear band structure and a periodic perturbation of the potential yields new small gaps. Novel gap solitons with $O(1)$ velocity despite the deep grating are presented in these gaps. An approximation of gap solitons is given by slowly varying envelopes which satisfy a system of generalized coupled mode equations (gCME) and by Bloch waves at the crossing point. The eigenspace at the crossing point is two dimensional and it is necessary to select Bloch waves belonging to the two band functions. This is achieved by an optimization algorithm. Traveling solitary wave solutions of the gCME then result in nearly solitary wave solutions of the PNLS moving at an $O(1)$ velocity across the periodic structure...