利用一类辅助方程求解(1+1)维KdV-Burgers方程的精确孤立波解
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摘要
经过对三类辅助方程引入解的特殊展开式途径的研究,进一步拓广了辅助方程法,并对关键操作步骤进行了改进,从而借助数学符号计算系统Mathematica给出(1+1)维KdV-Burgers方程的多个精确孤立波解.本文方法还可用于其它非线性方程的求解问题.
The auxiliary equation by introducing a special expansion for the solution of the three auxiliary equation and the mian procedures of the auxiliary equation method are also improved.Exact solitary wave solutions and perlodic wave solutions of the(1+1)-dimensional KdV-Burgers equation.are abtained with help of the symbolic computation system Mathematic and the method can be used to solve other nonlinear equations.
The auxiliary equation by introducing a special expansion for the solution of the three auxiliary equation and the mian procedures of the auxiliary equation method are also improved.Exact solitary wave solutions and perlodic wave solutions of the(1+1)-dimensional KdV-Burgers equation.are abtained with help of the symbolic computation system Mathematic and the method can be used to solve other nonlinear equations.
引文
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[2]Zhaqilao,Zhi-Bin Li,Darboux transformation and bidirectional soliton solutions of a new(2+1)-dimensional soliton equation[J].Physics Letters A 372(2008):1422~1428.
[3]Zheng Xue-Dong,Chen Yong,Li Biao,and Zhang Hong-Qing,A new generalization of extended Tanh-Function method for solving nonlinear evolution[J].Theor Phys(Beijing,China),2003,39:647~652.
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[5]M L Wang,solitary wave solutions for variant Boussiesq equations[J].Phys Lett A,1995,199:169~172.
[6]Fu Zun-Tao,Liu Shi-Kuo,and Liu Shi-Da,A new approach to solve nonlinear wave equation[J].Theor Phys(Beijing,China),2003,3:27~30.
[7]Liu Shi-Kuo,Fu Zun-Tao,Liu Shi-Da and Zhao Qiang,Expansion method about the Jacobi elliptic function and its applications to nonlinear wave equations[J].Acta phys Sin,2001,50(11):2068~2073.
[8]Zhang Jin-Liang,Ren Dong-Feng,Wang Ming-Liang,etc,The periodic wave solutions for the generalized NozhnikNovikov-Veselov equation[J].Chinese physics,2003,12(8):825.
[9]Sirendaoreji and S jiong,Auxiliary equation method and its applications to nonlinear evolution equations[J].International Journal of Modern Physics C,2003,14(8):1075~1085.
[10]Zhaqilao and LI Zhi-Bin,Multiple Periodic-Soliton Solutions for(3+1)-Dimensional Jimbo-Miwa Equation[J].Commun Theor Phys.(Beijing,China),2008,50:1036~1040.
[11]Zhang Jie-Fang,Wu Feng-Min,Bcklund transformation and multiple soliton solutions for the(3+1)-dimensional Jimbo-Miiwa equation[J].Chin Phys,2002,11(5):425~428.
[12]Guiqiong Xu,The soliton solutions,dromions of the Kadomtsev-Petviashvili and Jimbo-Miwa equations in(3+1)-dimensions[J].Chaos,Solitons and Fractals,Volume 30,Issue 1,October 2006:71~76.
[13]X Y.Tang,Z F Liang,Variable separation solutions for the(3+1)-dimensional Jimbo-Miwa equation[J].Physics Letters A,Volume 351,Issue 6,13 March 2006:398~402.
[2]Zhaqilao,Zhi-Bin Li,Darboux transformation and bidirectional soliton solutions of a new(2+1)-dimensional soliton equation[J].Physics Letters A 372(2008):1422~1428.
[3]Zheng Xue-Dong,Chen Yong,Li Biao,and Zhang Hong-Qing,A new generalization of extended Tanh-Function method for solving nonlinear evolution[J].Theor Phys(Beijing,China),2003,39:647~652.
[4]Weiss J,Tabor M and Catnevale G.The painleve property for partial differential equations[J].Math Phys,1983,24:522~526.
[5]M L Wang,solitary wave solutions for variant Boussiesq equations[J].Phys Lett A,1995,199:169~172.
[6]Fu Zun-Tao,Liu Shi-Kuo,and Liu Shi-Da,A new approach to solve nonlinear wave equation[J].Theor Phys(Beijing,China),2003,3:27~30.
[7]Liu Shi-Kuo,Fu Zun-Tao,Liu Shi-Da and Zhao Qiang,Expansion method about the Jacobi elliptic function and its applications to nonlinear wave equations[J].Acta phys Sin,2001,50(11):2068~2073.
[8]Zhang Jin-Liang,Ren Dong-Feng,Wang Ming-Liang,etc,The periodic wave solutions for the generalized NozhnikNovikov-Veselov equation[J].Chinese physics,2003,12(8):825.
[9]Sirendaoreji and S jiong,Auxiliary equation method and its applications to nonlinear evolution equations[J].International Journal of Modern Physics C,2003,14(8):1075~1085.
[10]Zhaqilao and LI Zhi-Bin,Multiple Periodic-Soliton Solutions for(3+1)-Dimensional Jimbo-Miwa Equation[J].Commun Theor Phys.(Beijing,China),2008,50:1036~1040.
[11]Zhang Jie-Fang,Wu Feng-Min,Bcklund transformation and multiple soliton solutions for the(3+1)-dimensional Jimbo-Miiwa equation[J].Chin Phys,2002,11(5):425~428.
[12]Guiqiong Xu,The soliton solutions,dromions of the Kadomtsev-Petviashvili and Jimbo-Miwa equations in(3+1)-dimensions[J].Chaos,Solitons and Fractals,Volume 30,Issue 1,October 2006:71~76.
[13]X Y.Tang,Z F Liang,Variable separation solutions for the(3+1)-dimensional Jimbo-Miwa equation[J].Physics Letters A,Volume 351,Issue 6,13 March 2006:398~402.