For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits t...For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits the Painleve property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation （DT） is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed： （i） Propagation of one soliton and two-peak soliton; （ii） Elastic interactions of the parabolic two solitons; （iii） Overlap two head-on solitons and two head-on two-peak solitons; （v） Two （vi） Decomposition phenomenon of one soliton into two solitons. phenomenon between two solitons; （iv） Collision of different types of interactions of the three solitons; ultrashort-pulse propagation in the inhomogeneous multi-component The results might be useful in the study on the nonlinear media.展开更多
The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explici...The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.60772023by the Open Fund No.BUAA-SKLSDE-09KF-04+2 种基金Supported Project No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsby the National Basic Research Program of China (973 Program) under Grant No.2005CB321901by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
文摘For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium, a system of coupled equations is analytically studied in this paper. Painleve analysis shows that this system admits the Painleve property under some constraints. By means of the Ablowitz-Kaup-Newell-Segur procedure, the Lax pair of this system is derived, and the Darboux transformation （DT） is constructed with the help of the obtained Lax pair. With symbolic computation, the soliton solutions are obtained by virtue of the DT algorithm. Figures are plotted to illustrate the dynamical features of the soliton solutions. Characteristics of the solitons propagating in an inhomogeneous multi-component nonlinear medium are discussed： （i） Propagation of one soliton and two-peak soliton; （ii） Elastic interactions of the parabolic two solitons; （iii） Overlap two head-on solitons and two head-on two-peak solitons; （v） Two （vi） Decomposition phenomenon of one soliton into two solitons. phenomenon between two solitons; （iv） Collision of different types of interactions of the three solitons; ultrashort-pulse propagation in the inhomogeneous multi-component The results might be useful in the study on the nonlinear media.
基金Supported by the National Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11675146
文摘The consistent tanh expansion(CTE) method is applied to the(2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution,and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlev′e truncated expansion method.And we investigate interactive properties of solitons and periodic waves.
