A general integrable three-component coupled nonlocal nonlinear Schrödinger equation

In this paper, we investigate a general integrable three-component coupled nonlocal nonlinear Schrödinger system with the parity-time symmetry. The general Nth Darboux transformation for this equation is constructed by proposing its Lax pair and infinitely many conservation laws. By using the Darboux transformation, its soliton solutions are obtained. Finally, we concretely discuss the dynamics of the obtained soliton solutions, which are also demonstrated by some figures.

[1]  C. Bender,et al.  Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry , 1997, physics/9712001.

[2]  M. Segev,et al.  Observation of parity–time symmetry in optics , 2010 .

[3]  Tao Xu,et al.  Localized waves in three-component coupled nonlinear Schrödinger equation , 2016 .

[4]  Lei Wang,et al.  Soliton solutions for the reduced Maxwell–Bloch system in nonlinear optics via the N-fold Darboux transformation , 2012 .

[5]  Boling Guo,et al.  Darboux transformation and multi-dark soliton for N-component nonlinear Schrödinger equations , 2013, 1309.1037.

[6]  V. Matveev,et al.  Darboux Transformations and Solitons , 1992 .

[7]  Wenjun Liu,et al.  Types of coefficient constraints of coupled nonlinear Schrödinger equations for elastic and inelastic interactions between spatial solitons with symbolic computation , 2014 .

[8]  Z. Musslimani,et al.  Optical Solitons in PT Periodic Potentials , 2008 .

[9]  Mohammad-Ali Miri,et al.  Observation of defect states in PT-symmetric optical lattices. , 2013, Physical review letters.

[10]  Min Li,et al.  Dark and antidark soliton interactions in the nonlocal nonlinear Schrödinger equation with the self-induced parity-time-symmetric potential. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  Holger Cartarius,et al.  Model of a PT-symmetric Bose-Einstein condensate in a delta-function double-well potential , 2012, 1203.1885.

[12]  Chen-Yuan Chen,et al.  WiFi assisted NAT traversal scheme for surveillance patrol robot , 2014 .

[13]  M. Ablowitz,et al.  Integrable discrete PT symmetric model. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  S. Billings,et al.  Spatial frequency range analysis for the nonlinear Schrödinger equation , 2014 .

[15]  X. Geng,et al.  Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation , 2012 .

[16]  Mohammad-Ali Miri,et al.  Continuous and discrete Schrödinger systems with parity-time-symmetric nonlinearities. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[17]  R. Morandotti,et al.  Observation of PT-symmetry breaking in complex optical potentials. , 2009, Physical review letters.

[18]  Li-Chen Zhao,et al.  Rogue-wave solutions of a three-component coupled nonlinear Schrödinger equation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  S. Longhi,et al.  Bloch oscillations in complex crystals with PT symmetry. , 2009, Physical review letters.

[20]  T. Wettig,et al.  Non-Hermitian Random Matrix Theory and Lattice QCD with Chemical Potential , 1999 .

[21]  Zuo-Nong Zhu,et al.  Solitons and dynamics for a general integrable nonlocal coupled nonlinear Schrödinger equation , 2017, Commun. Nonlinear Sci. Numer. Simul..

[22]  Boling Guo,et al.  Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations , 2014, Commun. Nonlinear Sci. Numer. Simul..

[23]  Lingling Zhang,et al.  The nonautonomous N-soliton solutions for coupled nonlinear Schrödinger equation with arbitrary time-dependent potential , 2017 .

[24]  U. Peschel,et al.  Parity–time synthetic photonic lattices , 2012, Nature.