In this paper, exact solutions are derived for four coupled complex nonlinear different equations by using simplified transformation method and algebraic equations.
The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the funct...In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.展开更多
In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The pr...In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.展开更多
With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ ...With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ my ＋ nt ＋ Г（x,y, t） for the （2＋1）-dimensional generalized Calogero-Bogoyavlenskii-Schiff system （GCBS） are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.展开更多
文摘In this paper, exact solutions are derived for four coupled complex nonlinear different equations by using simplified transformation method and algebraic equations.
基金Project supported by the National Nature Science Foundation of China （Grant No 49894190） of the Chinese Academy of Science （Grant No KZCXI-sw-18）, and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
基金Supported by the Natural Natural Science Foundation of China(Grant No:11361040)Science Research Foundation of Institution of Higher Education of Inner Mongolia Autonomous Region,China(Grant No:NJZY16180)Natural Science Foundation of Inner Mongolia Autonomous Region,China(Grant No:2015MS0128)。
文摘In this paper,new infinite sequence complex solutions of the coupled Kd V equations are constructed with the help of function transformation and the second kind of elliptic equation.First of all,according to the function transformation,the coupled Kd V equations are changed into the second kind of elliptic equation.Secondly,the new solutions and Bäcklund transformation of the second kind of elliptic equation are applied to search for new infinite sequence complex solutions of the coupled Kd V equations.These solutions include new infinite sequence complex solutions composed by Jacobi elliptic function,hyperbolic function and triangular function.
基金Project supported by the Natural Science Foundation of Inner Mongolia of China (Grant No. 20080404MS0104)the Young Scientists Fund of Inner Mongolia University of China (Grant No. ND0811)
文摘In this paper, the genera]ised two-dimensiona] differentia] transform method （DTM） of solving the time-fractiona] coupled KdV equations is proposed. The fractional derivative is described in the Caputo sense. The presented method is a numerical method based on the generalised Taylor series expansion which constructs an analytical solution in the form of a polynomial. An illustrative example shows that the genera]ised two-dimensional DTM is effective for the coupled equations.
基金supported by the National Natural Science Foundation of China(Grant No.11375079)the Scientific Research Fund of Zhejiang Provincial Education Department of China(Grant No.Y 201120994)the Natural Science Foundation of Zhejiang Province,China(Grant Nos.Y6100257,LY14A010005,and Y6110140)
文摘With the help of the symbolic computation system, Maple and Riccati equation （ξ＇ = ao ＋ a1ξ＋ a2ξ2）, expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx ＋ my ＋ nt ＋ Г（x,y, t） for the （2＋1）-dimensional generalized Calogero-Bogoyavlenskii-Schiff system （GCBS） are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.
