With linearly coupled nonlinear Schrodinger equations,numerical analysis has been performed on the mode locking forming procedure of a fiber laser in the linear cavity configuration.The fiber is Yb-doped multi-core ph...With linearly coupled nonlinear Schrodinger equations,numerical analysis has been performed on the mode locking forming procedure of a fiber laser in the linear cavity configuration.The fiber is Yb-doped multi-core photonic crystal fiber and semiconductor saturable absorber mirror(SESAM) is adopted as the nonlinear transmission element to start mode locking.Because of the noise randomness,initial pulse would be picked out by SESAM in one or more cores which makes the multi-core mode locking quite different from single-core one.The two situations are compared and fully discussed.Mode locking in multi-core photonic crystal fiber laser can be realized only if the couple coefficient between the cores and the temporal overlap between the pulses in different cores are large enough.展开更多
The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie gr...The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.展开更多
Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite differ...Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.展开更多
基金supported by National Basic Research Program of China (2006CB806002 and 2010CB327604)the National Natural Science Foundation of China (60838004 and 60978022)+2 种基金the Key Project of Chi-nese Ministry of Education (108032)the Foundation for the Author of National Excellent Doctoral Dissertation of China (2007B34)the Program for New Century Excellent Talents in University (NCET-07-0597)
文摘With linearly coupled nonlinear Schrodinger equations,numerical analysis has been performed on the mode locking forming procedure of a fiber laser in the linear cavity configuration.The fiber is Yb-doped multi-core photonic crystal fiber and semiconductor saturable absorber mirror(SESAM) is adopted as the nonlinear transmission element to start mode locking.Because of the noise randomness,initial pulse would be picked out by SESAM in one or more cores which makes the multi-core mode locking quite different from single-core one.The two situations are compared and fully discussed.Mode locking in multi-core photonic crystal fiber laser can be realized only if the couple coefficient between the cores and the temporal overlap between the pulses in different cores are large enough.
基金supported by the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institutethe National Natural Science Foundation of China under Grant Nos. 10735030 and 90503006
文摘The symmetries, symmetry reductions, and exact solutions of a coupled nonlinear Schrodinger （CNLS） equation derived from the governing system for atmospheric gravity waves are researched by means of classical Lie group approach in this paper. Calculation shows the CNLS equation is invariant under some Galilean transformations, scaling transformations, phase shifts, and space-time translations. Some ordinary differential equations are derived from the CNLS equation. Several exact solutions including envelope cnoidal waves, solitary waves and trigonometric function solutions for the CNLS equation are also obtained by making use of symmetries.
基金Supported by the National Natural Science Foundation of China under Grant No.91130013Hunan Provincial Innovation Foundation under Grant No.CX2012B010+1 种基金the Innovation Fund of National University of Defense Technology under Grant No.B120205the Open Foundation of State Key Laboratory
文摘Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.
