Exact states in waveguides with periodically modulated nonlinearity

E. Ding, H. N. Chan, K. W. Chow, Kaliyaperumal Nakkeeran, B. A. Malomed

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Abstract

We introduce a one-dimensional model based on the nonlinear Schrodinger/GrossPitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. Numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. Exact dark-bright soliton complex
in a coupled system with a localized modulation structure is also briefly considered . The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.
Original languageEnglish
Article number54002
JournalEurophysics Letters
Volume119
Issue number5
DOIs
Publication statusPublished - 27 Nov 2017

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nonlinearity
waveguides
modulation
solitary waves
numerical stability
Bose-Einstein condensates
optical waveguides
form factors

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Exact states in waveguides with periodically modulated nonlinearity. / Ding, E.; Chan, H. N.; Chow, K. W.; Nakkeeran, Kaliyaperumal; Malomed, B. A.

In: Europhysics Letters, Vol. 119, No. 5, 54002, 27.11.2017.

Research output: Contribution to journalArticle

Ding, E. ; Chan, H. N. ; Chow, K. W. ; Nakkeeran, Kaliyaperumal ; Malomed, B. A. / Exact states in waveguides with periodically modulated nonlinearity. In: Europhysics Letters. 2017 ; Vol. 119, No. 5.
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AU - Ding, E.

AU - Chan, H. N.

AU - Chow, K. W.

AU - Nakkeeran, Kaliyaperumal

AU - Malomed, B. A.

N1 - Partial financial support has been provided by the Research Grants Council (Hong Kong) contract HKU 17200815.

PY - 2017/11/27

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AB - We introduce a one-dimensional model based on the nonlinear Schrodinger/GrossPitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi dn function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. Numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. Exact dark-bright soliton complexin a coupled system with a localized modulation structure is also briefly considered . The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.

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