Browsing by Subject "Equivalence transformations"
Now showing items 1-20 of 23
-
Article
Conservation laws and hierarchies of potential symmetries for certain diffusion equations
(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 ...
-
Article
Differential invariants for quasi-linear and semi-linear wave-type equations
(2008)In this paper, we consider the class of wave-type equations utt = f (x, t, u) uxx + g (x, t, u, ux, ut) and two special cases of it. We derive the equivalence transformations for these equations and using these transformations, ...
-
Article
Differential invariants for systems of linear hyperbolic equations
(2010)In this paper we consider a general class of systems of two linear hyperbolic equations. Motivated by the existence of the Laplace invariants for the single linear hyperbolic equation, we adopt the problem of finding ...
-
Article
Differential invariants for third-order evolution equations
(2015)We consider a general class of third order evolution equations. We construct differential invariants with the employment of the infinitesimal method that using equivalence groups. We use the differential invariants to ...
-
Article
Enhanced group analysis and conservation laws of variable coefficient reaction-diffusion equations with power nonlinearities
(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 ...
-
Article
Enhanced group classification of Benjamin–Bona–Mahony–Burgers equations
(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. ...
-
Article
Enhanced group classification of Gardner equations with time-dependent coefficients
(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 ...
-
Article
Extended group analysis of variable coefficient reaction-diffusion equations with exponential nonlinearities
(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 ...
-
Article
Group analysis of (2 + 1)- and (3 + 1)-dimensional diffusion-convection equations
(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. ...
-
Conference Object
Group analysis of a class of nonlinear Kolmogorov equations
(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 ...
-
Article
Group analysis of Benjamin - Bona - Mahony equations with time dependent coefficients
(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 ...
-
Article
Group analysis of nonlinear fin equations
(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 ...
-
Article
Group analysis of variable coefficient diffusion-convection equations. I. Enhanced group classification
(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 ...
-
Article
Invariants of two- and three-dimensional hyperbolic equations
(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 ...
-
Article
Laplace type invariants for variable coefficient mKdV equations
(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. ...
-
Article
Numerical investigation of the nonlinear heat diffusion equation with high nonlinearity on the boundary
(2008)A nonlinear heat diffusion problem is considered when the thermal conductivity and heat capacity are nonlinear functions of the temperature. At one of the boundaries a highly nonlinear condition is imposed involving both ...
-
Article
Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries
(2014)The exhaustive group classification of a class of variable coefficient generalized KdV equations is presented, which completes and enhances results existing in the literature. Lie symmetries are used for solving an initial ...
-
Article
On linearization of hyperbolic equations using differential invariants
(2008)In this paper we consider the general class of hyperbolic equations ux t = F (x, t, u, ux, ut). We use equivalence transformations to derive differential invariants for this class and for two subclasses. Then we employ ...
-
Article
On linearizing systems of diffusion equations
(2006)We consider systems of diffusion equations that have considerable interest in Soil Science and Mathematical Biology and focus upon the problem of finding those forms of this class that can be linearized. In particular we ...
-
Article
On the group classification of variable-coefficient nonlinear diffusion-convection equations
(2006)We consider the variable coefficient diffusion-convection equation of the form f (x) ut = [g (x) D (u) ux]x + h (x) K (u) ux which has considerable interest in mathematical physics, biology and chemistry. We present a ...