Horseshoes for coupled discrete nonlinear Schroedinger equations

Journal Article · Sun Feb 15 00:00:00 EST 2009 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3077226· OSTI ID:21175998

Shieh, S -F ^[1]

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1. Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China)

In this paper, we study the spatial disorder of coupled discrete nonlinear Schroedinger (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.

• OSTI ID: 21175998
• Journal Information: Journal of Mathematical Physics, Vol. 50, Issue 2; Other Information: DOI: 10.1063/1.3077226; (c) 2009 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
OSCILLATIONS
SCHROEDINGER EQUATION
TOPOLOGY