Spatial properties and numerical solitary waves of a nonintegrable discrete nonlinear Schrodinger equation with nonlinear hopping
Spatial properties and numerical solitary waves of a nonintegrable discrete nonlinear Schrodinger equation with nonlinear hopping
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具有非线性跳跃的不可积离散非线性薛定谔方程的空间性质和数值孤立波
DOI：
10.1016/j.amc.2017.03.047
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发表时间：
2017
影响因子：
4
通讯作者：
Zhu Zuo-Nong
中科院分区：
文献类型：
--
作者：
Ma Li-Yuan;Zhu Zuo-Nong
本文研究了一类具有非线性跳跃的不可积离散非线性薛定谔方程。利用平面非线性动力学映射方法，研究了不可积dNLS方程的空间性质。通过构造不可积dNLS方程的定态形式的平面非线性映射的精确周期1和周期2轨道，得到了不可积dNLS方程的空间周期解。我们还给出了平面非线性映射轨道的数值模拟，并展示了非线性跳跃项对这些轨道的影响。利用离散傅立叶变换方法，我们得到了不可积dNLS方程的定常孤立波解和行进孤立波解的数值逼近。
In this paper, we study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with nonlinear hopping. By using the planar nonlinear dynamical map approach, we address the spatial properties of the nonintegrable dNLS equation. Through the constructions of exact period-1 and period-2 orbits of a planar nonlinear map which is a stationary version of the nonintegrable dNLS equation, we obtain the spatially periodic solutions of the nonintegrable dNLS equation. We also give the numerical simulations of the orbits of the planar nonlinear map and show how the nonlinear hopping terms affect those orbits. By using discrete Fourier transformation method, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation.