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 A hunter-gatherer–farmer population model: Lie symmetries, exact solutions and their interpretation

2018 ◽  
Vol 30 (2) ◽  
pp. 338-357 ◽  
Author(s):  
R. M. CHERNIHA ◽  
V. V. DAVYDOVYCH
Keyword(s):  
Exact Solutions ◽  
Population Model ◽  
Reaction Diffusion ◽  
Lie Symmetry ◽  
Lie Symmetries ◽  
System Modelling ◽  
Hunter Gatherers ◽  
Three Component Reaction ◽  
Biological Interpretation

The Lie symmetry classification of the known three-component reaction–diffusion system modelling the spread of an initially localized population of farmers into a region occupied by hunter-gatherers is derived. The Lie symmetries obtained for reducing the system in question to systems of ordinary differential equations (ODEs) and constructing exact solutions are applied. Several exact solutions of travelling front type are also found, their properties are identified and biological interpretation is discussed.

scholarly journals Third-Order Conditional Lie–Bäcklund Symmetries of Nonlinear Reaction-Diffusion Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Keqin Su ◽  
Jie Cao
Keyword(s):  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Governing Equations ◽  
Third Order ◽  
Differential Constraints ◽  
The Third ◽  
Nonlinear Reaction

The third-order conditional Lie–Bäcklund symmetries of nonlinear reaction-diffusion equations are constructed due to the method of linear determining equations. As a consequence, the exact solutions of the resulting equations are derived due to the compatibility of the governing equations and the admitted differential constraints, which are resting on the characteristic of the admitted conditional Lie–Bäcklund symmetries to be zero.

Conservation Laws and Exact Solutions with Symmetry Reduction of Nonlinear Reaction Diffusion Equations

2015 ◽  
Vol 16 (3-4) ◽  
pp. 191-196 ◽  
Author(s):  
Filiz Tascan ◽  
Arzu Yakut
Keyword(s):  
Differential Equations ◽  
Conservation Laws ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Lie Point Symmetries ◽  
Important Place ◽  
Physical Problems ◽  
Nonlinear Reaction

AbstractIn this work we study one of the most important applications of symmetries to physical problems, namely the construction of conservation laws. Conservation laws have important place for applications of differential equations and solutions, also in all physics applications. And so, this study deals conservation laws of first- and second-type nonlinear (NL) reaction diffusion equations. We used Ibragimov’s approach for finding conservation laws for these equations. And then, we found exact solutions of first- and second-type NL reaction diffusion equations with Lie-point symmetries.

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