TY - JOUR
T1 - Exact states in waveguides with periodically modulated nonlinearity
AU - Ding, E.
AU - Chan, H. N.
AU - Chow, K. W.
AU - Nakkeeran, K.
AU - Malomed, B. A.
N1 - Publisher Copyright:
© EPLA, 2017.
PY - 2017/9
Y1 - 2017/9
N2 - We introduce a one-dimensional model based on the nonlinear Schrödinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi 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. A 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. The 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.
AB - We introduce a one-dimensional model based on the nonlinear Schrödinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi 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. A 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. The 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.
UR - http://www.scopus.com/inward/record.url?scp=85040027674&partnerID=8YFLogxK
U2 - 10.1209/0295-5075/119/54002
DO - 10.1209/0295-5075/119/54002
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AN - SCOPUS:85040027674
SN - 0295-5075
VL - 119
JO - Journal de Physique (Paris), Lettres
JF - Journal de Physique (Paris), Lettres
IS - 5
M1 - 54002
ER -