Browsing by Author "Popovych, R. O."
Now showing items 1-8 of 8
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Conservation laws and hierarchies of potential symmetries for certain diffusion equations
Ivanova, Nataliya M.; Popovych, R. O.; Sophocleous, Christodoulos; Vaneeva, Olena O. (2009)We show that the so-called hidden potential symmetries considered in a recent paper [M.L. Gandarias, New potential symmetries for some evolution equations, Physica A 387 (2008) 2234-2242] are ordinary potential symmetries ...
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Article
Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities
Vaneeva, Olena O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, Christodoulos (2007)A class of variable coefficient (1 + 1)-dimensional nonlinear reaction-diffusion equations of the general form f (x) ut = (g (x) un ux)x + h (x) um is investigated. Different kinds of equivalence groups are constructed ...
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Article
Enhanced group analysis and exact solutions of variable coefficient semilinear diffusion equations with a power source
Vaneeva, Olena O.; Popovych, R. O.; Sophocleous, Christodoulos (2009)A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings between classes of differential ...
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Article
Exact solutions of a remarkable fin equation
Popovych, R. O.; Sophocleous, Christodoulos; Vaneeva, Olena O. (2008)A model 'remarkable' fin equation is singled out from a class of nonlinear (1 + 1)-dimensional fin equations. For this equation a number of exact solutions are constructed by means of using both the classical Lie algorithm ...
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Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities
Vaneeva, Olena O.; Popovych, R. O.; Sophocleous, Christodoulos (2012)The group classification of a class of variable coefficient reaction-diffusion equations with exponential nonlinearities is carried out up to both the equivalence generated by the corresponding generalized equivalence group ...
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Group analysis of Benjamin - Bona - Mahony equations with time dependent coefficients
Vaneeva, Olena O.; Popovych, R. O.; Sophocleous, Christodoulos (2015)Group classification of a class of Benjamin-Bona-Mahony (BBM) equations with time dependent coefficients is carried out. Two equivalent lists of equations possessing Lie symmetry extensions are presented: up to point ...
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Article
Group analysis of nonlinear fin equations
Vaneeva, Olena O.; Johnpillai, A. G.; Popovych, R. O.; Sophocleous, Christodoulos (2008)Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. These enable us to simplify the classification ...
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Article
Group analysis of variable coefficient diffusion-convection equations. I. Enhanced group classification
Ivanova, Nataliya M.; Popovych, R. O.; Sophocleous, Christodoulos (2010)We discuss the classical statement of group classification problem and some its extensions in the general case. After that, we carry out the complete extended group classification for a class of (1 + 1)-dimensional nonlinear ...