Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation,since dark solitons can be applied in waveguide optics as dynamic switches and junction...Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation,since dark solitons can be applied in waveguide optics as dynamic switches and junctions or optical logic devices.Based on the Lax pair,the binary Darboux transformation is constructed under certain constraints,thus the multi-dark soliton solutions are presented.Soliton propagation and collision are graphically discussed with the group-velocity dispersion,third-and fourth-order dispersions,which can affect the solitons’velocities but have no effect on the shapes.Elastic collisions between the two dark solitons and among the three dark solitons are displayed,while the elasticity cannot be influenced by the above three coefficients.展开更多
The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time-...The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.展开更多
The generalized binary Darboux transformation for the （1 ＋2）-dimensional non-isospectral KP-H equation is presented. Moreover, as a direct application, the new rogue wave solutions for the （1＋2）-dimensional non-...The generalized binary Darboux transformation for the （1 ＋2）-dimensional non-isospectral KP-H equation is presented. Moreover, as a direct application, the new rogue wave solutions for the （1＋2）-dimensional non-isospectral KP-II equation are constructed by the generalized binary Darboux transformation.展开更多
In this paper,we study the discrete Darboux and standard binary Darboux transformation for the generalized lattice Heisenberg magnet model.We calculate the quasi-Grammian solutions by the iteration of standard binary ...In this paper,we study the discrete Darboux and standard binary Darboux transformation for the generalized lattice Heisenberg magnet model.We calculate the quasi-Grammian solutions by the iteration of standard binary Darboux transformation.Furthermore,we derive the explicit matrix solutions for the binary Darboux matrix and then reduce them to the elementary Darboux matrix and plot the dynamics of solutions.展开更多
基金supported by the National Natural Science Foundation of China under grant no.11905061by the Fundamental Research Funds for the Central Universities(No.9161718004)。
文摘Dark solitons in the inhomogeneous optical fiber are studied in this manuscript via a higher-order nonlinear Schr?dinger equation,since dark solitons can be applied in waveguide optics as dynamic switches and junctions or optical logic devices.Based on the Lax pair,the binary Darboux transformation is constructed under certain constraints,thus the multi-dark soliton solutions are presented.Soliton propagation and collision are graphically discussed with the group-velocity dispersion,third-and fourth-order dispersions,which can affect the solitons’velocities but have no effect on the shapes.Elastic collisions between the two dark solitons and among the three dark solitons are displayed,while the elasticity cannot be influenced by the above three coefficients.
基金The project supported by the National Fundamental Research Program of China(973 Program)under Grant No.2007CB814800National Natural Science Foundation of China under Grant No.10601028
文摘The coupled Korteweg-de Vries （CKdV） equation with self-consistent sources （CKdVESCS） and its Lax representation are derived. We present a generalized binary Darboux transformation （GBDT） with an arbitrary time- dependent function for the CKdVESCS as well as the formula for the N-times repeated GBDT. This GBDT provides non-auto-Biicklund transformation between two CKdVESCSs with different degrees of sources and enables us to construct more generM solutions with N arbitrary t-dependent functions. We obtain positon, negaton, complexiton, and negaton- positon solutions of the CKdVESCS.
基金Supported by the National Natural Science Foundation of China under Grant No. 11061003 and Guangxi Natural Science Foundation under Grant No. 2013GXNSFAA019001
文摘The generalized binary Darboux transformation for the （1 ＋2）-dimensional non-isospectral KP-H equation is presented. Moreover, as a direct application, the new rogue wave solutions for the （1＋2）-dimensional non-isospectral KP-II equation are constructed by the generalized binary Darboux transformation.
文摘In this paper,we study the discrete Darboux and standard binary Darboux transformation for the generalized lattice Heisenberg magnet model.We calculate the quasi-Grammian solutions by the iteration of standard binary Darboux transformation.Furthermore,we derive the explicit matrix solutions for the binary Darboux matrix and then reduce them to the elementary Darboux matrix and plot the dynamics of solutions.
