李婷;沃维丰;

• 1:宁波大学数学系

摘要(Abstract)：

利用经典李群方法对Gd KP方程进行Lie对称分析,求得该方程的Lie对称代数,及其相应的约化方程和最优系统.更进一步,作者求出了d KP方程的部分群不变解.该方法在物理中有广泛的应用.

关键词(KeyWords)： GdKP方程;李群方法;对称约化;最优系统

Abstract:

Keywords:

基金项目(Foundation): 国家自然科学基金(11201249);; 浙江省自然基金(LY16A010002);; 宁波大学科研基金(XKL14D2040)

作者(Authors): 李婷;沃维丰;

参考文献(References)：

• [1]楼森岳,唐晓燕.非线性数学物理方法[M].北京:科学出版社,2006.
• [2]Bluman G W,Kumei S.Symmetries and Differential Equations[M].New York:Springer,1989.
• [3]Olver P.Applications of Lie Groups to Differential Equations[M].2nd ed.New York:Springer,1993.
• [4]Clakson P A,Kruskal M D.New similarity reductions of the Boussinesq equations[J].J.Math.Phys.,1989,30:2201.
• [5]Konopelchenko B,Martinez Alonso L,Ragnisco O.The-?-approach for the dispersionless KP hierarchy[J].J.Phys.A:Math.Gen.,2001,34:10209-10217.
• [6]Kadomtsev B B,Petviashvili V I.On the stability of solitary waves in weakly dispersive media[J].Sov.Phys.Dokl.,1970,15:539-41.
• [7]Ablowitz M J,Clarkson P A.Solitons,Nonlinear Evolution Equations and Inverse Scattering(London Math.Society Lecture Note Series vol 194)[M].Cambridge:Cambridge University Press,1991.
• [8]Ramirez J,Romero J L,Tracina R.Some new solutions for the Derrida-Lebowitz-Speer-Spohnequation[J].Com.Nonl.Sci.Num.Simu.,2013,18:2388-2397.
• [9]Hu X R,Chen Y.Two-dimensional symmetry reduction of(2+1)-dimensional nonlinear Klein-Gordon equation[J].Appl.Math.Comp.,2009,215:1141-1145.
• [10]Chou K S,Li G X.A note on optimal systems for the heat equation[J].J.Math.Anal.Appl.,2001,261:741-751.
• [11]Chou K S,Qu C Z.Optimal systems and group classification of(1+1)-dimensional heat equation[J].Acta.Appl.Math.,2004,83:257-287.
• [12]Qu C Z,Huang Q.Symmetry reductions and exact solutions of the affine heat equation[J].J.Math.Anal.Appl.,2008,346:521-530.
• [13]Coggeshall S V,Meyer-ter-Vehn J.Group-invariant solutions and optimal systems for multidimensional hydrodynamics[J].J.Math.Phys.,1992,33:585-3601.
• [14]Abdulwahhab M A.Optimal system and exact solutions for the generalized system of 2-dimensional Burgers equations with infinite Reynolds number[J].Com.Nonl.Sci.Num.Simu.,2015,20:98-112.
• [15]Hu X R,Li Y Q,Chen Y.The construction of two-dimensional optimal systems for the invariant solutions[J].ar Xiv,2014,1411:3798v1.
• [16]Qu C Z.Symmetries and solutions to the thin film equations[J].J.Math.Anal.Appl.,2006,317:381-397.
• [17]Ovsiannikov L V.Group Analysis of Differential Equations[M].New York:Academic Press,1982.