GEOMETRIC INVESTIGATION OF NONLINEAR REACTION-DIFFUSION-CONVECTION EQUATIONS: FISHER EQUATION AND ITS EXTENSIONS

2021 ◽  
Vol 24 (2) ◽  
pp. 145-151
Author(s):  
Atefeh Hasan-Zadeh
Keyword(s):  
Reaction Diffusion ◽  
Fisher Equation ◽  
Nonlinear Reaction ◽  
Diffusion Convection

Direct approach to a group classification problem: Fisher equation with time-dependent coefficients

2016 ◽  
Vol 30 (28n29) ◽  
pp. 1640021
Author(s):  
Motlatsi Molati ◽  
Chaudry Masood Khalique
Keyword(s):  
Reaction Diffusion ◽  
Classification Problem ◽  
Lie Symmetry ◽  
Group Classification ◽  
Time Dependent ◽  
Model Parameters ◽  
Fisher Equation ◽  
Lie Symmetry Analysis ◽  
Physical Systems ◽  
Diffusion Convection

We perform Lie symmetry analysis of a time-variable coefficient Fisher equation which models reaction–diffusion–convection phenomena in biological, chemical and physical systems. These time-dependent coefficients (model parameters or arbitrary elements) are specified via the direct integration of the classifying relations.

Symmetries, ansätze and exact solutions of nonlinear second-order evolution equations with convection terms, II

2006 ◽  
Vol 17 (5) ◽  
pp. 597-605 ◽  
Author(s):  
ROMAN CHERNIHA ◽  
MYKOLA SEROV
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Applied Mathematics ◽  
Reaction Diffusion ◽  
Second Order ◽  
Lie Symmetries ◽  
Nonlinear Reaction ◽  
Diffusion Convection ◽  
Natural Way

New results concerning Lie symmetries of nonlinear reaction-diffusion-convection equations, which supplement in a natural way the results published in the European Journal of Applied Mathematics (9(1998) 527–542) are presented.

scholarly journals Residual power series method for solving nonlinear reaction-diffusion-convection problems

2021 ◽  
Vol 39 (3) ◽  
pp. 177-188
Author(s):  
Maisa Khader ◽  
Mahmoud H. DarAssi
Keyword(s):  
Power Series ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Series Method ◽  
Power Series Method ◽  
Residual Power Series Method ◽  
Nonlinear Reaction ◽  
Residual Power Series ◽  
Diffusion Convection ◽  
Residual Power

In this paper, the residual power series method (RPSM) is applied to one of the most frequently used models in engineering and science, a nonlinear reaction diffusion convection initial value problems. The approximate solutions using the RPSM were compared to the exact solutions and to the approximate solutions using the homotopy analysis method.

scholarly journals ON THE INTEGRABILITY, BÄCKLUND TRANSFORMATION AND SYMMETRY ASPECTS OF A GENERALIZED FISHER TYPE NONLINEAR REACTION–DIFFUSION EQUATION

2004 ◽  
Vol 14 (05) ◽  
pp. 1577-1600 ◽  
Author(s):  
P. S. BINDU ◽  
M. LAKSHMANAN ◽  
M. SENTHILVELAN
Keyword(s):  
Bäcklund Transformation ◽  
Reaction Diffusion ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Reaction Diffusion Equation ◽  
Theoretical Interpretation ◽  
Fisher Equation ◽  
Backlund Transformation ◽  
Lie Symmetry Analysis ◽  
Nonlinear Reaction

The dynamics of nonlinear reaction–diffusion systems is dominated by the onset of patterns, and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlevé singularity structure analysis singles out a special case (m=2) as integrable. More interestingly, a Bäcklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same m=2 case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of traveling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.

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