应用李无穷小不变规则,得到了广义变系数KdV-Burgers方程的连续等价变换.从等价代数开始,构造了一阶微分不变量并依据微分不变量对方程作了群分类.最后,通过等价变换将一般的变系数KdV-Burgers方程映射为常系数Burgers方程、KdV方程、KdV-Burgers方程.同时,也得到了变系数KdV-Burgers方程的一些精确解.
参考文献
| [1] | Johnson R S.A nonlinear equation incorporating damping and dispersion[J].Fluid Mech.,1970,42:49-60. |
| [2] | Chen Y Z,Ding X W.Exact travelling wave solutions of nonlinear evolution equations in(1+1)and(2+1) dimensions[J].Nonlinear Analysis,2005,61(6):1005-1013. |
| [3] | Jeffrey A,Xu S Q.Exact solutions to the Korteweg-de Vrice-Burgers equation[J].Wave Motion,1989,11(6):559-564. |
| [4] | Jeffrey A.Mohamad M N B.Exact solutions to the KdV-Burgers equation[J].Wave Motion,1991,14(4):369-375. |
| [5] | 5 Demiray H.A note Oil the exact travelling wave solution to the KdV-Burgers equation[J].Wave Motion,2003,38(4):367-369. |
| [6] | Feng Z S.Traveling solitrary wave solutions to evolution equations with nonlinear terms of any order[J].Chaos,Solutions & Fractals,2003,17(5):861-868. |
| [7] | Chow K W,Grimshaw R H J,Ding E.Interactions of breathers and solutions in the extended Korteweg-de Vrice equation[J].Wave Motion,2005,43(2):158-166. |
| [8] | Ibragimov N H.Elementary Lie Group Analysis and Ordinary Differential Equations[M].New York:Wiley Press,1999. |
| [9] | Ibragimov N H.Infinitesimal method in the theory of invariants of algebraic and differential equations[J].Not.South Afr.Math.Soc.,1997,29:61-70. |
| [10] | Ovsiannikov L V.Group Analysis of Differential Equations[M].New York:Academic Press,1982,15-24. |
| [11] | Ibragimov N H,Torrisi M,Valenti A.Differential invariants of nonlinear equations[J].Nonlinear Science and Numerical Simulation,2004,9(1):69-80. |
| [12] | Senthilvelan M,Torrisi M,Valeuti A.Equivalence transformations and differential invariants of a generalized nonlinear Schrodinger equation[J].Mathematics and General,2006,39(14):3703-3713. |
| [13] | Tian Chou.Applications of Lie Group Method to Partial Differential Equation[M].Beijing:Science and Technology Press,2001.248-268(in Chinese). |
| [14] | Dong Zhongzhou,Yu Xichang,et al.Exact travelling wave solutions of nonlinear coupled KdV equations[J].Chinese Journal of Quantum Electronics(量子电子学报),2006,23(3):379-382(in Chinese). |
| [15] | Demiray H.A complex travelling wave solution to the KdV-Burgers equation[J].Phys.Lett.A,2005,344(6):418-422. |
| [16] | Tian Guichen,Liu Xiqiang.Exact solutions of the general variable coefficient KdV equation with external force term[J].Chinese Journal of Quantum Electronics(量子电子学报),2005,22(3):339-343(in Chinese). |
| [17] | Hilmi D.A travelling wave solution to the KdV-Burgers equation[J].Applied Mathematics and Computation,2004,154(3):665-670. |
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