Bifurcations and stability of gap solitons in periodic potentials

Dmitry E. Pelinovsky; Andrey A. Sukhorukov; Yuri S. Kivshar

doi:10.1103/PhysRevE.70.036618

Bifurcations and stability of gap solitons in periodic potentials

Dmitry E. Pelinovsky^*, Andrey A. Sukhorukov, Yuri S. Kivshar

^*Corresponding author for this work

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

146 Citations (Scopus)

Abstract

The existence, internal modes and stability of gap solitons in nonlinear periodic systems are discussed. The bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum are also discussed. It is found that gap solitons can appear near all upper or lower band edges of the spectrum, for defocusing or focusing nonlinearity, respectively. The results show that two types of gap solitons can bifurcate from each band edge and one out of those two is always unstable.

Original language	English
Article number	036618
Pages (from-to)	036618-1-036618-17
Journal	Physical Review E
Volume	70
Issue number	3 2
DOIs	https://doi.org/10.1103/PhysRevE.70.036618
Publication status	Published - Sept 2004

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10.1103/PhysRevE.70.036618

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abstract = "The existence, internal modes and stability of gap solitons in nonlinear periodic systems are discussed. The bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum are also discussed. It is found that gap solitons can appear near all upper or lower band edges of the spectrum, for defocusing or focusing nonlinearity, respectively. The results show that two types of gap solitons can bifurcate from each band edge and one out of those two is always unstable.",

author = "Pelinovsky, {Dmitry E.} and Sukhorukov, {Andrey A.} and Kivshar, {Yuri S.}",

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AU - Kivshar, Yuri S.

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N2 - The existence, internal modes and stability of gap solitons in nonlinear periodic systems are discussed. The bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum are also discussed. It is found that gap solitons can appear near all upper or lower band edges of the spectrum, for defocusing or focusing nonlinearity, respectively. The results show that two types of gap solitons can bifurcate from each band edge and one out of those two is always unstable.

AB - The existence, internal modes and stability of gap solitons in nonlinear periodic systems are discussed. The bifurcations of gap solitons from the band edges of the Floquet-Bloch spectrum are also discussed. It is found that gap solitons can appear near all upper or lower band edges of the spectrum, for defocusing or focusing nonlinearity, respectively. The results show that two types of gap solitons can bifurcate from each band edge and one out of those two is always unstable.

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Bifurcations and stability of gap solitons in periodic potentials

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