Generalized Symmetries and mCK Method Analysis of the (2+1)-Dimensional Coupled Burgers Equations

In this paper, generalized symmetries and mCK method are employed to analyze the (2+1)-dimensional coupled Burgers equations. Firstly, based on the generalized symmetries method, the corresponding symmetries of the (2+1)-dimensional coupled Burgers equations are derived. And then, using the mCK method, symmetry transformation group theorem is presented. From symmetry transformation group theorem, a great many of new solutions can be derived. Lastly, Lie algebra for given symmetry group are considered.

[1]  P. Olver.  Applications of Lie Groups to Differential Equations , 1986 .

[2]  Lei Ya,et al.  Finite symmetry transformation group and localized structures of the (2+1)-dimensional coupled Burgers equation , 2013 .

[3]  Wen-Xiu Ma,et al.  A hierarchy of coupled Burgers systems possessing a hereditary structure , 1993 .

[4]  Abdul-Majid Wazwaz.  Multiple kink solutions for M-component Burgers equations in (1+1)-dimensions and (2+1)-dimensions , 2010, Appl. Math. Comput..

[5]  Abdul-Majid Wazwaz,et al.  Multiple kink solutions and multiple singular kink solutions for the (2 + 1)-dimensional Burgers equations , 2008, Appl. Math. Comput..

[6]  A. Biswas,et al.  TOPOLOGICAL SOLITONS AND CONSERVATION LAWS OF THE COUPLED BURGERS EQUATIONS , 2014 .

[7]  Abdul-Majid Wazwaz,et al.  Multiple-front solutions for the Burgers equation and the coupled Burgers equations , 2007, Appl. Math. Comput..

[8]  Ting Su,et al.  Explicit solutions for a modified 2+1-dimensional coupled Burgers equation by using Darboux transformation , 2017, Appl. Math. Lett..

[9]  A. Kara,et al.  Soliton Solutions and Group Analysis of a New Coupled (2 + 1)-Dimensional Burgers Equations , 2015 .

[10]  Xi-Qiang Liu,et al.  Symmetry reduction, exact solutions and conservation laws of a new fifth-order nonlinear integrable equation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[11]  K. M. Tamizhmani,et al.  Similarity reductions and painlevé property of the coupled higher dimensional Burgers' equation , 1991 .

[12]  D. Baleanu,et al.  Lie symmetry analysis and conservation laws for the time fractional simplified modified Kawahara equation , 2018, Open Physics.

[13]  Hongqing Zhang,et al.  A new coupled sub-equations expansion method and novel complexiton solutions of (2+1)-dimensional Burgers equation , 2007, Appl. Math. Comput..

[14]  Hong-Cai Ma,et al.  LETTER TO THE EDITOR: Non-Lie symmetry groups of (2+1)-dimensional nonlinear systems obtained from a simple direct method , 2005 .

[15]  Dumitru Baleanu,et al.  New exact solutions of Burgers’ type equations with conformable derivative , 2017 .