### Abstract

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 language | English |
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Article number | 54002 |

Journal | Europhysics Letters |

Volume | 119 |

Issue number | 5 |

DOIs | |

Publication status | Published - 27 Nov 2017 |

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### Cite this

*Europhysics Letters*,

*119*(5), [54002]. https://doi.org/10.1209/0295-5075/119/54002

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

Research output: Contribution to journal › Article

*Europhysics Letters*, vol. 119, no. 5, 54002. https://doi.org/10.1209/0295-5075/119/54002

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TY - JOUR

T1 - Exact states in waveguides with periodically modulated nonlinearity

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

Y1 - 2017/11/27

N2 - 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.

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.

U2 - 10.1209/0295-5075/119/54002

DO - 10.1209/0295-5075/119/54002

M3 - Article

VL - 119

JO - Europhysics Letters

JF - Europhysics Letters

SN - 0295-5075

IS - 5

M1 - 54002

ER -