In this work,using the Hirota bilinear method,N-soliton solution is obtained for Hirota-Satsuma nonlinear evolution equation:u_t - u_(xxt) - 3u_xu_t + u_x = 0.
These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper,...These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper, the generalized bilinear method instead of the Hirota bilinear method is used to obtain the rational solutions to the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli-like equation (hereinafter referred to as BLMP equation). Meanwhile, the (2 + 1)-dimensional BLMP-like equation is derived on the basis of the generalized bilinear operators D3,x D3,y and D3,t. And the rational solutions to the (2 + 1)-dimensional BLMP-like equation are obtained successively. Finally, with the help of the N-soliton solutions of the (2 + 1)-dimensional BLMP equation, the interactions of the N-soliton solutions can be derived. The results show that the two soliton still maintained the original waveform after happened collision.展开更多
Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-...Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-1 wy)=0 in view of a different treatment.展开更多
Integrable discretizations of are proposed. N-soliton solutions for analogues of the complex and real Dym the complex and real Dym equations both semi-discrete and fully discrete equations are also presented.
基金Foundation item： Supported by the Natural Science Foundation of China（61072147, 11071159） Supported by the Shanghai Leading Academic Discipline Project（J50101） Supported by the Youth Foundation of Zhoukou Normal University（zknuqn200917）
文摘In this work,using the Hirota bilinear method,N-soliton solution is obtained for Hirota-Satsuma nonlinear evolution equation:u_t - u_(xxt) - 3u_xu_t + u_x = 0.
基金supported by the National Natural Science Foundation of China(11301454and 11271168)the Natural Science Foundation for Colleges and Universities in Jiangsu Province(13KJD110009)the Youth Foundation of Suzhou Vocational University(2010SZDQ11)
文摘These rational solutions which can be described a kind of algebraic solitary waves which have great potential in applied value in atmosphere and ocean. It has attracted more and more attention recently. In this paper, the generalized bilinear method instead of the Hirota bilinear method is used to obtain the rational solutions to the (2 + 1)-dimensional Boiti-Leon-Manna-Pempinelli-like equation (hereinafter referred to as BLMP equation). Meanwhile, the (2 + 1)-dimensional BLMP-like equation is derived on the basis of the generalized bilinear operators D3,x D3,y and D3,t. And the rational solutions to the (2 + 1)-dimensional BLMP-like equation are obtained successively. Finally, with the help of the N-soliton solutions of the (2 + 1)-dimensional BLMP equation, the interactions of the N-soliton solutions can be derived. The results show that the two soliton still maintained the original waveform after happened collision.
基金Supported by the National Natural Science Foundation of China（10871132 11074160） Supported by the National Natura Science Foundation of Henan Province（102300410190 092300410202）
文摘Using the Hirota's bilinear method,some new N-soliton solution are presented for two multidimensional analogues of the m-KdV equation wt+wxxx-6w 2 wx+3 2( w x -1 wy+w-x -1 wz)x=0 and wt+wxxx?6w 2 wx+3 2( wwy+wx-x-1 wy)=0 in view of a different treatment.
文摘Integrable discretizations of are proposed. N-soliton solutions for analogues of the complex and real Dym the complex and real Dym equations both semi-discrete and fully discrete equations are also presented.
基金Project supported by the National Natural Science Foundations of China(11001250,11331008)the Foundation for Young Teachers in Colleges and Universities of Henan Province(2013GGJS-010)the Soft Science Foundation of Science and Technology Department of Henan Province(142400410274)
