Browsing by Author "Sophocleous, Christodoulos"
Now showing items 61-80 of 90
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On linearizing systems of diffusion equations
Sophocleous, Christodoulos; Wiltshire, R. J. (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 ...
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On point transformations of a generalised Burgers equation
Kingston, John G.; Sophocleous, Christodoulos (1991)This Letter classifies all finite point transformations between generalised Burgers equations of the form ut + uux + a(t)uxx = 0. These transformations necessarily include in particular all the well-known invariant ...
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On point transformations of generalized nonlinear diffusion equations
Pallikaros, Christakis Andrea; Sophocleous, Christodoulos (1995)This paper classifies all finite point transformations of a general class between generalized diffusion equations of the form ut=x 1-M [xN-1f(u)ux]x. These transformations may be divided into three cases, depending on the ...
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On shear deformable beam theories: The frequency and normal mode equations of the homogeneous orthotropic bickford beam
Soldatos, Kostas P.; Sophocleous, Christodoulos (2001)This paper provides a step forwards the construction and documentation of the frequency equations and the characteristic functions of a general three-degrees-of-freedom theory that describes the plane motion of shear ...
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On symmetries of radially symmetric nonlinear diffusion equation
Sophocleous, Christodoulos (1992)In this paper symmetries are sought for radially symmetric nonlinear diffusion equations of the type ut=r1-N[r N-1f(u)ur]r. The nonlinear forms of this equation which admit Lie classical symmetries are completely classified ...
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On the classification of similarity solutions of a two-dimensional diffusion-advection equation
Demetriou, Ellie; Christou, Marios Andreas; Sophocleous, Christodoulos (2007)We consider the two-dimensional diffusion-advection equation ut = Duyy - frac(d k, d u) ux. We present the classification of Lie symmetries of this equation. For the case k(u) = u2 we give the complete list of similarity ...
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On the group classification of variable-coefficient nonlinear diffusion-convection equations
Ivanova, Nataliya M.; Sophocleous, Christodoulos (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 ...
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On the invariants of two dimensional linear parabolic equations
Tsaousi, Christina; Sophocleous, Christodoulos; Tracinà, Rita (2012)We consider the most general two dimensional linear parabolic equations. Motivated by the recent work of Ibragimov et al. [1-3] we construct differential invariants, semi-invariants and invariant equations. These results ...
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On the simplification of the form of Lie transformation groups admitted by systems of evolution differential equations
Kontogiorgis, Stavros; Sophocleous, Christodoulos (2017)For a system of two partial differential equations in two independent variables the Lie point symmetry generator has the form τ(t,x,u,v)∂t+ξ(t,x,u,v)∂x+η(t,x,u,v)∂u+μ(t,x,u,v)∂v. We consider a system of evolution equations ...
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Photorefractive accelerating pulses
Parker, D. F.; Sophocleous, Christodoulos; Radha, Ch (2002)The existence of similarity reductions having x - 2Vz - kz2 as similarity variable is demonstrated for a number of evolution systems arising in optoelectronics. The parameter k (≠0) corresponds to acceleration if z represents ...
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Potential symmetries of inhomogeneous nonlinear diffusion equations
Sophocleous, Christodoulos (2000)In this paper potential symmetries are sought of the inhomogeneous nonlinear diffusion equations ut = x1-M [xN-1 f(u)ux]x. The functional forms of f(u) that admit such symmetries are completely classified. A complete list ...
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Potential symmetries of nonlinear diffusion-convection equations
Sophocleous, Christodoulos (1996)In this paper potential symmetries are sought for the nonlinear diffusion-convection equations ut = [f(u)ux]x - [k(u)]x. The functional forms of f(u) and k(u) that admit such symmetries are completely classified.
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Pulse collisions and polarisation conversion for optical fibres
Sophocleous, Christodoulos; Parker, D. F. (1994)Axisymmetric fibres support linearly and circularly polarised sech pulses and also elliptically polarised pulses having more complicated profile. Collisions between any two such pulses are studied numerically. Large collision ...
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Seventh international workshop: Group analysis of differential equations and integrable systems (GADEISVII) olena vaneeva
Vaneeva, Olena O.; Sophocleous, Christodoulos; Popovych, R.; Boyko, V.; Damianou, Pantelis A. (2015)
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Similarity reductions of the (1 + 3)-dimensional Burgers equation
Christou, Marios Andreas; Ivanova, Nataliya M.; Sophocleous, Christodoulos (2009)We consider the (1 + 3)-dimensional Burgers equation ut = uxx + uyy + uzz + uux which has considerable interest in mathematical physics. We complete the list of similarity reductions that are obtained from the Lie symmetries ...
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Symmetries and form-preserving transformations of generalised inhomogeneous nonlinear diffusion equations
Sophocleous, Christodoulos (2003)We consider the variable coefficient inhomogeneous nonlinear diffusion equations of the form f(x)ut = [g(x)unux]x. We present a complete classification of Lie symmetries and form-preserving point transformations in the ...
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Symmetries and form-preserving transformations of one-dimensional wave equations with dissipation
Kingston, John G.; Sophocleous, Christodoulos (2001)General results are given for the forms of infinitesimal point symmetries of the class of partial differential equations in which utt is a function of x,t,u,ut and the x-derivatives of u up to order n ≥ 2. Continuous and ...
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Symmetries for certain coupled nonlinear Schrodinger equations
Sophocleous, Christodoulos (1994)Generalized symmetries are sought for certain coupled nonlinear Schrodinger equations. It is shown that all Lie-Backlund symmetries but one are equivalent to Lie point symmetries.
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Symmetries of Hamiltonian systems with two degrees of freedom
Damianou, Pantelis A.; Sophocleous, Christodoulos (1999)We classify the Lie point symmetry groups for an autonomous Hamiltonian system with two degrees of freedom. With the exception of the harmonic oscillator or a free particle where the dimension is 15, we obtain all dimensions ...
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Symmetry analysis for a class of nonlinear dispersive equations
Charalambous, Kyriakos; Sophocleous, Christodoulos (2015)A class of dispersive equations is studied within the framework of group analysis of differential equations. The enhanced Lie group classification is achieved. The complete list of equivalence transformations is presented. ...