The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infin...The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.展开更多
A hierarchy of integrable lattice soliton equations and its Hamiitonian struc ture associated a 3×3 matrix spectral problem are got. An integrable symplectic map is obtained by nonlinearization of Lax pairs and a...A hierarchy of integrable lattice soliton equations and its Hamiitonian struc ture associated a 3×3 matrix spectral problem are got. An integrable symplectic map is obtained by nonlinearization of Lax pairs and ad joint Lax pairs of the hierarchy. Moreover, the solutions to the prototype system of lattice equations in the hierarchy are reduced to the solutions of a system of ordinary differential equations and a simple iterative process of the symplectic map.展开更多
We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a wea...We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.展开更多
A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of c...A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of conservation laws were given for the corresponding hierarchy.展开更多
This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there alw...This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μc for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ 〉 μc. In the self-defocusing case, solitons exist only when μ 〈 μc. Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.展开更多
A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable sym...A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonli-nearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting lattice soliton equations.展开更多
基金supported in part by the National Natural Science Foundation of China (Grant Nos 60677030 and 60808002)the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant No 20060280007)+2 种基金the Science and Technology Commission of Shanghai Municipality, China (Grant No 06ZR14034)Ming Shen is also supported by the Australian Endeavor Research Fellowship scholarshipappreciates the hospitality of the Laser Physics Center during his stay in Canberra
文摘The propagation of spatial solitons is systematically investigated in nonlocal nonlinear media with an imprinted transverse periodic modulation of the refractive index. Based on the variational principle and the infinitesimal approximation of Maclaurin series expansion, we obtain an analytical solution of such nonlocal spatial solitons and an interesting result that the critical power for such solitons propagation is smaller than that in uniform nonlocal self-focusing media. It is found that there exist thresholds in modulation period and lattice depth for such solitons. A stable spatial soliton propagation is maintained with proper adjustment of the modulation period and the lattice depth.
文摘A hierarchy of integrable lattice soliton equations and its Hamiitonian struc ture associated a 3×3 matrix spectral problem are got. An integrable symplectic map is obtained by nonlinearization of Lax pairs and ad joint Lax pairs of the hierarchy. Moreover, the solutions to the prototype system of lattice equations in the hierarchy are reduced to the solutions of a system of ordinary differential equations and a simple iterative process of the symplectic map.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11547125 and 11465008the Hunan Provincial Natural Science Foundation under Grant Nos 2015JJ4020 and 2015JJ2114the Scientific Research Fund of Hunan Provincial Education Department under Grant No 14A118
文摘We investigate the stability and collision dynamics of dissipative matter-wave solitons formed in a quasi-one- dimensional Bose-Einstein condensate with linear gain and three-body recombination loss perturbed by a weak optical lattice. It is shown that the linear gain can modify the stability of the single dissipative soliton moving in the optical lattice. The collision dynamics of two individual dissipative matter-wave solitons explicitly depend on the linear gain parameter, and they display different dynamical behaviors in both the in-phase and out-of-phase interaction regimes.
基金Project supported by National Natural Science Fundation of China(Grant No .10371070)
文摘A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of conservation laws were given for the corresponding hierarchy.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 61308019) and the Foundation for Distinguished Young Talents in Higher Education of Guangdong (Grant No. Yq2013157). H. Wang also acknowledges the financial support from China Scholarship Council.
文摘This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μc for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ 〉 μc. In the self-defocusing case, solitons exist only when μ 〈 μc. Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.
文摘A hierarchy of lattice soliton equations is derived from a discrete matrix spectral problem. It is shown that the resulting lattice soliton equations are all discrete Liouville integrable systems. A new integrable symplectic map and a family of finite-dimensional integrable systems are given by the binary nonli-nearization method. The binary Bargmann constraint gives rise to a Backlund transformation for the resulting lattice soliton equations.