The generalized (n + 1)-dimensional KP equation with variable coefficients is investigated in this paper. The bilinear form of the equation has been obtained by the Hirota direct method. In addition, with the help of ...The generalized (n + 1)-dimensional KP equation with variable coefficients is investigated in this paper. The bilinear form of the equation has been obtained by the Hirota direct method. In addition, with the help of Wronskian technique and the Pfaffian properties, Wronskian and Grammian solutions have been generated.展开更多
The algebraic mapping relations between the(2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein–Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton ...The algebraic mapping relations between the(2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein–Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, "V" shape, "snake" shape and "M" shape solitary waves,Zigzag-curve type, "ω" shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions.展开更多
Exact solutions with three-wave form including three solitary wave, breather-type two-solitary wave, doubly breather-type of solitary wave, double-periodic kind of solitary wave are obtained using bilinear form and ex...Exact solutions with three-wave form including three solitary wave, breather-type two-solitary wave, doubly breather-type of solitary wave, double-periodic kind of solitary wave are obtained using bilinear form and extended threewave approach with the aid of Maple. It is important that completed elastic collision, non-completed elastic collision,and fusion of three waves are investigated, respectively.展开更多
文摘The generalized (n + 1)-dimensional KP equation with variable coefficients is investigated in this paper. The bilinear form of the equation has been obtained by the Hirota direct method. In addition, with the help of Wronskian technique and the Pfaffian properties, Wronskian and Grammian solutions have been generated.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant No.LZ15A050001the National Natural Science Foundation of China under Grant No.11175158
文摘The algebraic mapping relations between the(2+1)-dimensional double sine-Gordon equation and the cubic nonlinear Klein–Gordon equation are constructed. Many new types of two-dimensional resonant kink, bright soliton and solitoff solutions are obtained, such as broken line shape, "V" shape, "snake" shape and "M" shape solitary waves,Zigzag-curve type, "ω" shape, peroidic-curve type, oscillatory Arch-type and parabolic shape bright soliton waves. We also investigate the propagating properties of some soliton solutions.
基金Supported by National Natural Science Foundation of China under Grant No.11361048Sichuan Educational Science Foundation under Grant No.12ZB069
文摘Exact solutions with three-wave form including three solitary wave, breather-type two-solitary wave, doubly breather-type of solitary wave, double-periodic kind of solitary wave are obtained using bilinear form and extended threewave approach with the aid of Maple. It is important that completed elastic collision, non-completed elastic collision,and fusion of three waves are investigated, respectively.
