Browsing by Subject "Lie symmetries"
Now showing items 120 of 22

Article
Application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition
(2013)We demonstrate the power of symmetry in the resolution of some evolution partial differential equations which arise in various aspects of finance. The essential theme is that which Lie promulgated approximately 140 years ...

Article
A deductive approach to the solution of the problem of optimal pairs trading from the viewpoint of stochastic control with timedependent parameters
(2015)In a fairly recent paper (2008 American Control Conference, June 1113, 10351039), the problem of dealing with trading in optimal pairs was treated from the viewpoint of stochastic control. The analysis of the subsequent ...

Article
Enhanced group analysis and conservation laws of variable coefficient reactiondiffusion equations with power nonlinearities
(2007)A class of variable coefficient (1 + 1)dimensional nonlinear reactiondiffusion 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 Gardner equations with timedependent coefficients
(2015)We classify the Lie symmetries of variable coefficient Gardner equations (called also the combined KdVmKdV equations). In contrast to the particular results presented in Molati and Ramollo (2012) we perform the exhaustive ...

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), 6775, DOI 10.1007/s1066501295954]
(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 ...

Article
Extended group analysis of variable coefficient reactiondiffusion equations with exponential nonlinearities
(2012)The group classification of a class of variable coefficient reactiondiffusion 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 diffusionconvection equations
(2008)We perform the complete Lie group classification of a (2 + 1) and a (3 + 1)dimensional classes of nonlinear diffusionconvection 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 diffusionconvection equations (nonlinear Kolmogorov equations) with timedependent 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 BenjaminBonaMahony (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 classification of systems of diffusion equations
(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 ...

Article
Lie group analysis of twodimensional variablecoefficient Burgers equation
(2010)The modern group analysis of differential equations is used to study a class of twodimensional variable coefficient Burgers equations. The group classification of this class is performed. Equivalence transformations are ...

Article
Lie symmetries of generalized Burgers equations: application to boundaryvalue problems
(2015)There exist several approaches exploiting Lie symmetries in the reduction of boundaryvalue problems for partial differential equations modelling realworld phenomena to those problems for ordinary differential equations. ...

Article
Numerical similarity reductions of the (1+3)dimensional Burgers equation
(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 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 the classification of similarity solutions of a twodimensional diffusionadvection equation
(2007)We consider the twodimensional diffusionadvection 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 ...

Article
On the group classification of variablecoefficient nonlinear diffusionconvection equations
(2006)We consider the variable coefficient diffusionconvection 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 ...

Article
Similarity reductions of the (1 + 3)dimensional Burgers equation
(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 ...

Article
Symmetry analysis for a class of nonlinear dispersive equations
(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. ...

Article
Symmetry and singularity analyses of some equations of the fifth and sixth order in the spatial variable arising from the modelling of thin films
(2013)In the modelling of the flow of thin films higherorder derivatives in the spatial variable are introduced to model nonlinear effects. We examine nonlinear evolution equations of the fifth and sixth orders in the spatial ...