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^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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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10.1016/j.jmaa.2014.02.003

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@article{e6cdebfc3d4f4cf7864403a944d5afb1,

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",

author = "Shieh, {Shih Feng}",

note = "Funding Information: The author appreciates the anonymous referee for the valuable comments and suggestions. This work is partially supported by the National Science Council .",

year = "2014",

month = jul,

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doi = "10.1016/j.jmaa.2014.02.003",

language = "English",

volume = "415",

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journal = "Journal of Mathematical Analysis and Applications",

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publisher = "Academic Press Inc.",

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TY - JOUR

T1 - Characterization of soliton solutions in 2D nonlinear Schrödinger lattices by using the spatial disorder

AU - Shieh, Shih Feng

N1 - Funding Information: The author appreciates the anonymous referee for the valuable comments and suggestions. This work is partially supported by the National Science Council .

PY - 2014/7/15

Y1 - 2014/7/15

N2 - 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.

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.

KW - Bright solitons

KW - Discrete nonlinear schrödinger equation

KW - Horseshoe

KW - Soliton solution

KW - Spatial disorder

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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