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

Keywords

Bright solitons
Discrete nonlinear schrödinger equation
Horseshoe
Soliton solution
Spatial disorder

ASJC Scopus subject areas

Analysis
Applied Mathematics

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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.",

keywords = "Bright solitons, Discrete nonlinear schr{\"o}dinger equation, Horseshoe, Soliton solution, Spatial disorder",

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AB - 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.

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