Related papers: Extended group analysis of variable coefficient re…
Group classification of a class of nonlinear fin equations is carried out exhaustively. Additional equivalence transformations and conditional equivalence groups are also found. They allow to simplify results of classification and further…
The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome…
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 group…
Enhancing and essentially generalizing previous results on a class of (1+1)-dimensional nonlinear wave and elliptic equations, we apply several new techniques to classify admissible point transformations within this class up to the…
The exact renormalization group is applied to a nonlinear diffusion equation with a discontinuous diffusion coefficient. The generating functional of the solution for the initial-value problem of nonlinear diffusion equations is first…
The enhanced group classification of a semi-linear generalization of a general bond-pricing equation is carried out by employing the underlying equivalence and additional equivalence transformations. The knowledge of the sub classes with…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…
A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
We study admissible and equivalence point transformations between generalized multidimensional nonlinear Schr\"odinger equations and classify Lie symmetries of such equations. We begin with a wide superclass of Schr\"odinger-type equations,…
Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are classified and a theorem on connection of them with point ones…
We find the complete equivalence group of a class of (1+1)-dimensional second-order evolution equations, which is infinite-dimensional. The equivariant moving frame methodology is invoked to construct, in the regular case of the…
Given a class of differential equations with arbitrary element, the problems of symmetry group, nonclassical symmetry and conservation law classifications are to determine for each member the structure of its Lie symmetry group, conditional…
A class of nonlinear reaction-diffusion-convection equations describing various processes in physics, biology, chemistry etc. is under study in the case of time and two space variables. The group of equivalence transformations is…
We carry out group analysis of a class of generalized fifth-order Korteweg-de Vries equations with time dependent coefficients. Admissible transformations, Lie symmetries and similarity reductions of equations from the class are classified…
We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
We consider a system of reaction-diffusion equations describing the reversible reaction of two species $\mathcal{U}, \mathcal{V}$ forming a third species $\mathcal{W}$ and vice versa according to mass action law kinetics with arbitrary…
A definition of invariance in Lie's sense for a boundary value problem (BVP) with the basic evolution differential equations is proposed. A problem of group classification at a wide class of BVPs parameterized by arbitrary elements is…