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

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.

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

Received: 08 August 2013
Accepted manuscript online:

PACS:	02.20.Sv	(Lie algebras of Lie groups)
	02.30.Jr	(Partial differential equations)
	02.60.Cb	(Numerical simulation; solution of equations)
	04.20.Jb	(Exact solutions)

Corresponding Authors: R. K. Gupta
E-mail: rajeshgupta@thapar.edu

Cite this article:

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 2014 Chin. Phys. B 23 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

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