Browsing by Author "Sophocleous, Christodoulos"
Now showing items 21-40 of 90
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Article
Enhanced group classification of Benjamin–Bona–Mahony–Burgers equations
Vaneeva, Olena O.; Pošta, Severin; Sophocleous, Christodoulos (2017)A class of the Benjamin–Bona–Mahony–Burgers (BBMB) equations with time-dependent coefficients is investigated with the Lie symmetry point of view. The set of admissible transformations of the class is described exhaustively. ...
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Article
Enhanced group classification of Gardner equations with time-dependent coefficients
Vaneeva, Olena O.; Kuriksha, O.; Sophocleous, Christodoulos (2015)We classify the Lie symmetries of variable coefficient Gardner equations (called also the combined KdV-mKdV equations). In contrast to the particular results presented in Molati and Ramollo (2012) we perform the exhaustive ...
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Article
Enhanced Symmetry Analysis of Two-Dimensional Burgers System
Kontogiorgis, Stavros; Popovych, Roman O.; Sophocleous, Christodoulos (2019)We carry out enhanced symmetry analysis of a two-dimensional Burgers system. The complete point symmetry group of this system is found using an enhanced version of the algebraic method. Lie reductions of the Burgers system ...
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Article
Equivalence transformations in the study of integrability
Vaneeva, Olena O.; O Popovych, R.; Sophocleous, Christodoulos (2014)We discuss how point transformations can be used for the study of integrability, in particular, for deriving classes of integrable variable-coefficient differential equations. The procedure of finding the equivalence ...
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Article
Erratum: The application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition [J Eng Math, 82, (2013), 67-75, DOI 10.1007/s10665-012-9595-4]
O’Hara, J. G.; Sophocleous, Christodoulos; Leach, Peter G. L. (2015)In an analysis of the Lie point symmetries of the equation which allows for the inclusion of transaction costs into the Black–Scholes model (J Eng Math 82:67–75, 2013) one of the symmetries was omitted. We rectify that ...
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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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Article
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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Article
Further transformation properties of generalised inhomogeneous nonlinear diffusion equations with variable coefficients
Sophocleous, Christodoulos (2005)We consider the variable coefficient inhomogeneous nonlinear diffusion equations of the form xput = [xqu nux]x. We present further transformation properties for this nonlinear class of equations that do not appear in the ...
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Article
Group analysis of (2 + 1)- and (3 + 1)-dimensional diffusion-convection equations
Demetriou, Ellie; Ivanova, Nataliya M.; Sophocleous, Christodoulos (2008)We perform the complete Lie group classification of a (2 + 1)- and a (3 + 1)-dimensional classes of non-linear diffusion-convection equations. This classification generalizes and completes existing results in the literature. ...
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Conference Object
Group analysis of a class of nonlinear Kolmogorov equations
Vaneeva, Olena O.; Karadzhov, Y.; Sophocleous, Christodoulos (Springer New York LLC, 2016)A class of (1+2)-dimensional diffusion-convection equations (nonlinear Kolmogorov equations) with time-dependent coefficients is studied with Lie symmetry point of view. The complete group classification is achieved using ...
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Article
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 Benjamin—Bona—Mahony equations with time dependent coefficients
Vaneeva, Olena O.; Popovych, Roman O.; Sophocleous, Christodoulos (2015)
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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 ...
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Article
Group classification of a class of equations arising in financial mathematics
Ivanova, Nataliya M.; Sophocleous, Christodoulos; Leach, Peter G. L. (2010)We provide a group classification of a class of nonlinearisable evolution partial differential equations which arise in Financial Mathematics. Sixteen different cases are identified for the general problem and another seven ...
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Article
Group classification of systems of diffusion equations
Kontogiorgis, Stavros; Sophocleous, Christodoulos (2017)Group classification of a class of systems of diffusion equations is carried out. Arbitrary elements that appear in the system depend on two variables. All forms of the arbitrary elements that provide additional Lie ...
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Article
Group classification of variable coefficient K(m,n) equations
Charalambous, Kyriakos; Vaneeva, Olena O.; Sophocleous, Christodoulos (2014)Lie symmetries of K (m n ) equations with time-dependent coefficients ate classified Group classification is presented up to widest possible equivalence groups the usuil equivalence group of the whole class for the general ...
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Article
Hodograph-type transformations
Sophocleous, Christodoulos (2003)We consider second-order evolution equations of the form ut = F1(u,ux)uxx+F2(u,ux) and third order of the form ut = F1(u,ux)u xxx+F2(u,ux,uxx). For each of these equations we construct point transformations which relate ...
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Article
Invariants of two- and three-dimensional hyperbolic equations
Tsaousi, Christina; Sophocleous, Christodoulos; Tracinà, Rita (2009)We consider linear hyperbolic equations of the formut t = underover(∑, i = 1, n) uxi xi + underover(∑, i = 1, n) Xi (x1, ..., xn, t) uxi + T (x1, ..., xn, t) ut + U (x1, ..., xn, t) u . We derive equivalence transformations ...
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Article
Laplace type invariants for variable coefficient mKdV equations
Tsaousi, Christina; Tracinà, Rita; Sophocleous, Christodoulos (2015)We consider a class of variable-coefficient mKdV equations. We derive the equivalence transformations in the infinitesimal form and we employ them to construct differential invariants of the respective equivalence algebra. ...