Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

doi:10.1088/1674-1056/23/3/030201

中国物理B ›› 2014, Vol. 23 ›› Issue (3): 30201-030201.doi: 10.1088/1674-1056/23/3/030201

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Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

Vikas Kumar^a, R. K. Gupta^b, Ram Jiwari^b

a Department of Mathematics, D. A. V. College Pundari, Kaithal 136026, Haryana, India;
b School of Mathematics and Computer Applications, Thapar University, Patiala 147004, Punjab, India

收稿日期:2013-08-08 出版日期:2014-03-15 发布日期:2014-03-15

Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

Vikas Kumar^a, R. K. Gupta^b, Ram Jiwari^b

a Department of Mathematics, D. A. V. College Pundari, Kaithal 136026, Haryana, India;
b School of Mathematics and Computer Applications, Thapar University, Patiala 147004, Punjab, India

Received:2013-08-08 Online:2014-03-15 Published:2014-03-15
Contact: R. K. Gupta E-mail:rajeshgupta@thapar.edu

摘要/Abstract

摘要： In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (G’/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.

关键词: diffusion–, advection equation, Lie group analysis, numerical solutions, extended (G’, /G)-expansion method

Abstract: In this paper, the variable-coefficient diffusion-advection (DA) equation, which arises in modeling various physical phenomena, is studied by the Lie symmetry approach. The similarity reductions are derived by determining the complete sets of point symmetries of this equation, and then exact and numerical solutions are reported for the reduced second-order nonlinear ordinary differential equations. Further, an extended (G’/G)-expansion method is applied to the DA equation to construct some new non-traveling wave solutions.

Key words: diffusion–advection equation, Lie group analysis, numerical solutions, extended (G’/G)-expansion method

中图分类号: (Lie algebras of Lie groups)

02.20.Sv

02.30.Jr (Partial differential equations) 02.60.Cb (Numerical simulation; solution of equations) 04.20.Jb (Exact solutions)

Vikas Kumar, R. K. Gupta, Ram Jiwari. Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients[J]. 中国物理B, 2014, 23(3): 30201-030201.

参考文献 21

[1]	Olver P J 1993 Applications of Lie Groups to Differential Equations (Berlin: Springer)
[2]	Bluman G W and Kumei S 1989 Symmetries and Differential Equations (New York: Springer)
[3]	Ovsyannikov L V 1982 Group Analysis of Differential Equations (New York: Academic)
[4]	Demetriou E, ChristouMA and Sophocleous C 2007 Appl. Math. Comput. 187 1333
[5]	Singh K and Gupta R K 2006 Int. J. Eng. Sci. 44 241
[6]	Kumar S, Singh K and Gupta R K 2012 Commun. Nonlinear Sci. Numer. Simul. 17 1529
[7]	Gupta R K and Singh K 2011 Commun. Nonlinear Sci. Numer. Simul. 16 4189
[8]	Goyal N and Gupta R K 2012 Phys. Scr. 85 015004
[9]	Kumar V, Gupta R K and Jiwari R 2013 Chin. Phys. B 22 050201
[10]	Khalique C M and Adem K R 2011 Math. Comput. Model. 54 184
[11]	Johnpillai A G, Kara A H and Biswas A 2013 Appl. Math. Lett. 26 376
[12]	Kaur L and Gupta R K 2013 Math. Meth. Appl. Sci. 36 584
[13]	Gupta R K and Bansal A 2013 Appl. Math. Comput. 219 5290
[14]	Wang M L, Li X and Zhang 2008 J. Phys. Lett. A 372 417
[15]	Zhang S, Dong L, Ba J M and Sun Y N 2009 Phys. Lett. A 373 905
[16]	Guo S and Zhou Y 2010 Appl. Math. Comput. 215 3214
[17]	Li B Q and Ma Y L 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 144
[18]	Alexander F J and Lebowitz J L 1990 J. Phys. A: Math. Gen. 23 375
[19]	Alexander F J and Lebowitz J L 1994 J. Phys. A: Math. Gen. 27 683
[20]	Saied E A and Abd El-Rahman R G 1998 J. Stat. Phys. 94 639
[21]	Elwakil S A, Zahran M A and Sabry R 2005 ZAMP 56 986

Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

Lie group analysis, numerical and non-traveling wave solutions for the (2+1)-dimensional diffusion–advection equation with variable coefficients

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