Browsing by Author "Sophocleous, Christodoulos"
Now showing items 41-60 of 90
-
Article
Laplace type invariants for variable coefficient mKdV equations[ONLINE]
Tsaousi, Christina; Tracinà, Rita; Sophocleous, Christodoulos (2015)
-
Article
Lie group analysis of two-dimensional variable-coefficient Burgers equation
Ivanova, Nataliya M.; Sophocleous, Christodoulos; Tracinà, Rita (2010)The modern group analysis of differential equations is used to study a class of two-dimensional variable coefficient Burgers equations. The group classification of this class is performed. Equivalence transformations are ...
-
Conference Object
Lie Symmetries for Variable Coefficient Compound KdV-Burgers Equations
Charalambous, Kyriakos; Sophocleous, Christodoulos (2019)
-
Article
Lie symmetries of a system arising in plasma physics
Charalambous, Kyriakos; Sophocleous, Christodoulos (2018)Lie group classification for a diffusion-type system that has applications in plasma physics is derived. The classification depends on the values of 5 parameters that appear in the system. Similarity reductions are presented. ...
-
Article
Lie symmetries of generalized Burgers equations: application to boundary-value problems
Vaneeva, Olena O.; Sophocleous, Christodoulos; Leach, Peter G. L. (2015)There exist several approaches exploiting Lie symmetries in the reduction of boundary-value problems for partial differential equations modelling real-world phenomena to those problems for ordinary differential equations. ...
-
Conference Object
Lie Symmetry Analysis of a Third-Order Equation Arising from a General Class of Lotka–Volterra Chains
Charalambous, Kyriakos; Sophocleous, Christodoulos (Springer, 2018)In the literature has recently appeared a class of bi-cubic equations from the study of a general class of Lotka–Volterra chains. Lie symmetry analysis is performed for this non-linear partial differential equation and a ...
-
Article
Lie symmetry analysis of a variable coefficient Calogero–Degasperis equation
Sophocleous, Christodoulos; Tracinà, Rita (2018)We consider a general class of variable coefficient Calogero–Degasperis equations. The complete Lie group classification is performed with the aid of the appropriate equivalence group. Lie symmetries are used to derive a ...
-
Article
Lie symmetry analysis of Burgers-type systems
Kontogiorgis, Stavros; Sophocleous, Christodoulos (2018)Lie group classification for 2 Burgers-type systems is obtained. Systems contain 2 arbitrary elements that depend on the 2 dependent variables. Equivalence transformations for the systems are derived. Examples of nonclassical ...
-
Article
Linearisation and potential symmetries of certain systems of diffusion equations
Sophocleous, Christodoulos; Wiltshire, R. J. (2006)We consider systems of two pure one-dimensional diffusion equations that have considerable interest in Soil Science and Mathematical Biology. We construct non-local symmetries for these systems. These are determined by ...
-
Article
Linearizing mappings for certain nonlinear diffusion equations
Sophocleous, Christodoulos (1998)In this paper we consider the nonlinear diffusion equations of the type ut = x1-M[xN-1λ(u + u)-2ux]x. It is shown that linearizing point transformations do not exist. This equation can be equivalently written as a system ...
-
Article
Miura-type transformations
Sophocleous, Christodoulos (1992)Miura-type transformations are considered for generalized KdV equations of the form uy+uxxx+ integral (u,ux)=0. The nonlinear forms of this equation that admit such transformations are completely classified. For the same ...
-
Article
Noether and master symmetries for the Toda lattice
Damianou, Pantelis A.; Sophocleous, Christodoulos (2005)In this letter we examine the interrelation between Noether symmetries, master symmetries and recursion operators for the Toda lattice. The topics include invariants, higher Poisson brackets and the various relations they ...
-
Article
Numerical investigation of the nonlinear heat diffusion equation with high nonlinearity on the boundary
Christou, Marios Andreas; Sophocleous, Christodoulos; Christov, Christo I. (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 similarity reductions of the (1+3)-dimensional Burgers equation
Christou, Marios Andreas; Sophocleous, Christodoulos (2011)We consider the (1+3)-dimensional Burgers equation ut = u xx + uyy + uzz + uux which has considerable interest in mathematical physics. Lie symmetries are used to reduce it to certain ordinary differential equations. We ...
-
Article
Numerical similarity solution for a variable coefficient K(m, n) equation
Christou, Marios A.; Papanicolaou, Nectarios C.; Sophocleous, Christodoulos (2018)A technique for finding numerical similarity solutions to an initial boundary value problem (IBVP) for generalized K(m, n) equations is described. The equation under consideration is nonlinear and has variable coefficients. ...
-
Article
Numerical solutions of boundary value problems for variable coefficient generalized KdV equations using Lie symmetries
Vaneeva, Olena O.; Papanicolaou, N. C.; Christou, Marios Andreas; Sophocleous, Christodoulos (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 a sequence of higher-order nonlinear diffusion-convection equations
Charalambous, Kyriakos; Sophocleous, Christodoulos (2019)Motivated by the existence of the thin film equations, fourth and sixth order, which are generalizations of the diffusion equation, we consider a sequence of higher order nonlinear diffusion-convection equations. We ...
-
Article
On cyclic symmetries of n-dimensional nonlinear wave equations
Sophocleous, Christodoulos (2000)We consider the three n-dimensional nonlinear wave equations utt = k=1∑n[Fk(u)uxk]xk utt = k=1∑nFk(uxk)uxkxk and utt = k=1∑nFk(uxkxk). We also consider a special class of point transformations. Motivated by the results on ...
-
Article
On form-preserving point transformations of partial differential equations
Kingston, John G.; Sophocleous, Christodoulos (1998)New identities are presented relating arbitrary order partial derivatives of u(x, t) and u′(x′, t′) for the general point transformation x′ = P(x, t, u), t′ = Q(x, t, u), u′ = R(x, t, u). These identities are used to study ...
-
Article
On linearization of hyperbolic equations using differential invariants
Tsaousi, Christina; Sophocleous, Christodoulos (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 ...