Horseshoes for coupled discrete nonlinear Schrodinger equations

被引：4
|
作者：
Shieh, Shih-Feng [1 ]
机构：
[1] Natl Taiwan Normal Univ, Dept Math, Taipei 11677, Taiwan
来源：
JOURNAL OF MATHEMATICAL PHYSICS | 2009年 / 50卷 / 02期
关键词：
nonlinear differential equations; Schrodinger equation; WAVE; SEPARATION; SOLITONS; ARRAYS;
D O I：
10.1063/1.3077226
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
In this paper, we study the spatial disorder of coupled discrete nonlinear Schrodinger (CDNLS) equations with piecewise-monotone nonlinearities. By the construction of horseshoes, we show that the CDNLS equation possesses a hyperbolic invariant Cantor set on which it is topological conjugate to the full shift on N symbols. The CDNLS equation exhibits spatial disorder, resulting from the strong amplitudes and stiffness of the nonlinearities in the system. The complexity of the disorder is determined by the oscillations of the nonlinearities. We then apply our results to CDNLS equations with Kerr-like nonlinearity. We shall also show some patterns of the localized solutions of the CDNLS equation.
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页数：13
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