Soliton chaos in the nonlinear Schrödinger equation with spatially periodic perturbations.
Soliton chaos in the nonlinear Schrödinger equation with spatially periodic perturbations.
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DOI：
10.1103/physreva.46.r2973
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发表时间：
1992-09
期刊：
影响因子：
--
通讯作者：
Rainer Scharf;A. R. Bishop
中科院分区：
文献类型：
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作者：
Rainer Scharf;A. R. Bishop
我们用与时间无关的空间周期势扰动一维非线性薛定谔方程，该势的周期大于系统中存在的孤立子的空间宽度。集体坐标近似映射系统的不可积的多粒子动力学与有效的哈密顿量，我们得出的假设下，我们可以忽略三孤子碰撞以及两孤子碰撞消失的相对速度。我们给出了一个估计的功率由一个单独的孤子在扰动的存在下，并表明，辐射效应可以忽略不计的扰动与足够小的振幅和大的空间周期。我们表明，这种扰动的非线性薛定谔方程的不可积性已经体现在两个孤子部门。我们利用有效多粒子哈密顿量来研究孤子的脱钉。有效的哈密顿结果进行了比较与数值模拟的全扰动方程。
We perturb the one-dimensional nonlinear Schroedinger equation with a time-independent spatially periodic potential with a period large compared to the spatial width of solitons present in the system. A collective-coordinate approximation maps the system to a nonintegrable many-particle dynamics with an effective Hamiltonian, which we derive under the assumption that we can neglect three-soliton collisions as well as two-soliton collisions with vanishing relative velocity. We give an estimate for the power radiated by a single soliton in the presence of the perturbation and show that radiative effects can be neglected for perturbations with sufficiently small amplitude and large spatial period. We show that the nonintegrability of this perturbed nonlinear Schroedinger equation manifests itself already in the two-soliton sector. We use the effective many-particle Hamiltonian to investigate soliton depinning. The effective Hamiltonian results are compared with numerical simulations of the full perturbed equation.