Characterization of soliton solutions in 2D nonlinear Schrodinger lattices by using the spatial disorder

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:415

Article

Shieh, Shih-Feng

关键词: Discrete nonlinear Schrodinger equation;    Horseshoe;    Soliton solution;    Bright solitons;    Spatial disorder;   

DOI  :  10.1016/j.jmaa.2014.02.003

来源: Elsevier

【 摘 要 】

In this paper, the pattern of the soliton solutions to the discrete nonlinear Schrodinger (DNLS) equations in a 2D lattice is studied by the construction of horseshoes in l(infinity)-spaces. The spatial disorder of the DNLS equations is the result of the strong amplitudes and stiffness of the nonlinearities. The complexity of this disorder is log(N + 1) where N is the number of turning points of the nonlinearities. For the case N = 1, there exist disjoint intervals I-0 and I-1, for which the state u(m,n) at site (m,n) can be either dark (u(m,n) is an element of I-0) or bright (u(m,n) is an element of I-1) that depends on the configuration k(m,n) = 0 or 1, respectively. Bright soliton solutions of the DNLS equations with a cubic nonlinearity are also discussed. (C) 2014 Elsevier Inc. All rights reserved.

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