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

Shih Feng Shieh

doi:10.1016/j.jmaa.2014.02.003

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

Shih Feng Shieh

Department of Mathematics

Research output: Contribution to journal › Article

Abstract

In this paper, the pattern of the soliton solutions to the discrete nonlinear Schrödinger (DNLS) equations in a 2. D lattice is studied by the construction of horseshoes in l∞-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 I0 and I1, for which the state um,n at site (m,n) can be either dark (um,n∈I0) or bright (um,n∈I1) that depends on the configuration km,n=0 or 1, respectively. Bright soliton solutions of the DNLS equations with a cubic nonlinearity are also discussed.

Original language	English
Pages (from-to)	736-749
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	415
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.02.003
Publication status	Published - 2014 Jul 15

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Keywords

Bright solitons
Discrete nonlinear schrödinger equation
Horseshoe
Soliton solution
Spatial disorder

ASJC Scopus subject areas

Analysis
Applied Mathematics

Cite this

Shieh, S. F. (2014). Characterization of soliton solutions in 2D nonlinear Schrödinger lattices by using the spatial disorder. Journal of Mathematical Analysis and Applications, 415(2), 736-749. https://doi.org/10.1016/j.jmaa.2014.02.003

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title = "Characterization of soliton solutions in 2D nonlinear Schr{\"o}dinger lattices by using the spatial disorder",

abstract = "In this paper, the pattern of the soliton solutions to the discrete nonlinear Schr{\"o}dinger (DNLS) equations in a 2. D lattice is studied by the construction of horseshoes in l∞-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 I0 and I1, for which the state um,n at site (m,n) can be either dark (um,n∈I0) or bright (um,n∈I1) that depends on the configuration km,n=0 or 1, respectively. Bright soliton solutions of the DNLS equations with a cubic nonlinearity are also discussed.",

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10.1016/j.jmaa.2014.02.003