四阶非线性发展方程的精确解和广义条件对称Exact solutions and generalized conditional symmetries to fourth-order nonlinear evolution equations
郑群珍;姬利娜;
摘要(Abstract):
讨论了允许二阶广义条件对称的四阶非线性发展方程.通过广义条件对称方法得到了其对称约化和精确解.
关键词(KeyWords): 广义条件对称;四阶非线性发展方程;对称约化;精确解
基金项目(Foundation):
作者(Authors): 郑群珍;姬利娜;
参考文献(References):
- [1]King J R.Exact polynomial solutions to some nonlinear evolution equations[J].Phys.D.,1993,64:35-65.
- [2]King J R.Two generalizations of the thin film equation[J].Math.Comput.Mod.,2001,34:737-756.
- [3]Bluman G W,Kumei S.Symmetries and Differential Equations[M].NewYork:Springer,1989.
- [4]Olver P J.Applications of Lie Groups to Differential Equations[M].2nd ed.New York:Springer,1993.
- [5]Ibragimov N H.Transformation Groups Applied to Mathematical Physics[M].Boston:Reidel,1985.
- [6]Bluman G W,Cole J D.The general similarity solution of the heat equation[J].J.Math.Mech.,1969,18:1025-1042.
- [7]Clarkson P A,Kruskal M D.New similarity reductions of the Boussinesq equation[J].J.Math.Phys.,1989,30:2201-2213.
- [8]Lou S Y.A note on the new similarity reductions of the Boussinesq equation[J].Phys.Lett.A,1990,151:133-135.
- [9]Estevez P G.The direct method and the singular manifold method for the Fitzhugh-Nagumo equation[J].Phys.Lett.A,1992,171:259-261.
- [10]Fuschych P G,Zhdanov R Z.Anti-reduction and exact solutions of nonlinear heat equations[J].J.Nonl.Math.Phys.,1994,1:60-64.
- [11]Fokas A S,Liu Q M,Nonlinear interaction of traveling waves of nonintegrable equations[J].Phys.Rev.Lett.,1994,72:3293-3296.
- [12]Zhdanov R Z.Conditional Lie-Backlund symmetry and reductions of evolution equations[J].J.Phys.A:Math.Gen.,1995,28:3841-3850.
- [13]Qu C Z.Group classification and generalized conditional symmetry reduction of the nonlinear diffusion-convection equation with a nonlinear source[J].Stud.Appl.Math.,1997,99:107-136.
- [14]Qu C Z.Exact solutions to nonlinear diffusion equations obtained by a generalized conditional symmet-ry method[J].IMA J.Appl.Math.,1999,62:283-302.
- [15]Qu C Z.Classification and reduction of some systems of quasilinear partial differential equations[J].Nonlin.Anal.TMA,2000,42:301-327.
- [16]Qu C Z,Zhang S L,Liu R C.Separation of variables and exact solutions to quasilinear diffusionequations with nonlinear source[J].Physica D.,2000,144:97-123.
- [17]Zhang S L,Lou S Y,Qu C Z.New variable separation approach:application to nonlinear diffusionequations[J].J.Phys.A.Math.Gen.,2003,36:1223-1242.
- [18]Bertozzi A L,Brener M P,Dupont T F.Singularities and similarities ininterface flows,in:Sirovich L.,Trends and Perspectives in Applied Mathematics[M].New York:Springer-Verlag,1994.