Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

S. A. Elwakil; S. K. El-Labany; M. A. Zahran; R. Sabry

doi:10.1016/j.cpc.2004.01.001

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

S. A. Elwakil
, S. K. El-Labany
, M. A. Zahran
, R. Sabry

Mansoura University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D(u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K(u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m > 1 is the power of the nonlinear convection term).

Original language	English
Pages (from-to)	113-116
Number of pages	4
Journal	Computer Physics Communications
Volume	158
Issue number	2
DOIs	https://doi.org/10.1016/j.cpc.2004.01.001
State	Published - 1 Apr 2004
Externally published	Yes

Keywords

Diffusion-convection processes
Modified extended tanh-function method
Symbolic computations
Travelling wave solutions

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10.1016/j.cpc.2004.01.001

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title = "Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions",

abstract = "The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D(u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K(u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m > 1 is the power of the nonlinear convection term).",

keywords = "Diffusion-convection processes, Modified extended tanh-function method, Symbolic computations, Travelling wave solutions",

author = "Elwakil, \{S. A.\} and El-Labany, \{S. K.\} and Zahran, \{M. A.\} and R. Sabry",

year = "2004",

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doi = "10.1016/j.cpc.2004.01.001",

language = "English",

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journal = "Computer Physics Communications",

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T1 - Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

AU - Elwakil, S. A.

AU - El-Labany, S. K.

AU - Zahran, M. A.

AU - Sabry, R.

PY - 2004/4/1

Y1 - 2004/4/1

N2 - The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D(u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K(u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m > 1 is the power of the nonlinear convection term).

AB - The modified extended tanh-function method were applied to the general class of nonlinear diffusion-convection equations where the concentration-dependent diffusivity, D(u), was taken to be a constant while the concentration-dependent hydraulic conductivity, K(u) were taken to be in a power law. The obtained solutions include rational-type, triangular-type, singular-type, and solitary wave solutions. In fact, the profile of the obtained solitary wave solutions resemble the characteristics of a shock-wave like structure for an arbitrary m (where m > 1 is the power of the nonlinear convection term).

KW - Diffusion-convection processes

KW - Modified extended tanh-function method

KW - Symbolic computations

KW - Travelling wave solutions

UR - https://www.scopus.com/pages/publications/1642272414

U2 - 10.1016/j.cpc.2004.01.001

DO - 10.1016/j.cpc.2004.01.001

M3 - Article

AN - SCOPUS:1642272414

SN - 0010-4655

VL - 158

SP - 113

EP - 116

JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 2

ER -

Exact travelling wave solutions for a diffusion-convection equation in two and three spatial dimensions

Abstract

Keywords

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