相关论文: Complete group classification of a class of nonlin…
The complete group classification problem for the class of (1+1)-dimensional $r$th order general variable-coefficient Burgers-Korteweg-de Vries equations is solved for arbitrary values of $r$ greater than or equal to two. We find the…
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…
An exhaustive group classification of variable coefficient generalized Kawahara equations is carried out. As a result, we derive new variable coefficient nonlinear models admitting Lie symmetry extensions. All inequivalent Lie reductions of…
The group classification of a class of semilinear reaction-diffusion equations with exponential nonlinearity is carried out using the technique of mapping between classes, which was recently proposed in [O.O. Vaneeva, R.O. Popovych and C.…
We perform the complete group classification in the class of nonlinear Schr\"odinger equations of the form $i\psi_t+\psi_{xx}+|\psi|^\gamma\psi+V(t,x)\psi=0$ where $V$ is an arbitrary complex-valued potential depending on $t$ and $x,$…
A group classification of first-order delay ordinary differential equation (DODE) accompanied by an equation for delay parameter (delay relation) is presented. A subset of such systems (delay ordinary differential systems or DODSs) which…
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,…
In this paper, we consider group classification of local and quasi-local symmetries for a general fourth-order evolution equations in one spatial variable. Following the approach developed by Zhdanov and Lahno, we construct all inequivalent…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
A complete group classification of a class of variable coefficient (1+1)-dimensional telegraph equations $f(x)u_{tt}=(H(u)u_x)_x+K(u)u_x$, is given, by using a compatibility method and additional equivalence transformations. A number of new…
We revisit the entire framework of group classification of differential equations. After introducing the notion of weakly similar classes of differential equations, we develop the mapping method of group classification for such classes,…
In this paper we classify in terms of Lie point symmetries the three-dimensional nonrelativistic motion of charged particles in arbitrary time-independent electromagnetic fields. The classification is made on the ground of equivalence…
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…
Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the case of integral or integro-differential equations as well as…
Admissible point transformations of classes of $r$th order linear ordinary differential equations (in particular, the whole class of such equations and its subclasses of equations in the rational form, the Laguerre-Forsyth form, the first…
Methods for the design of physical parameterization schemes that possess certain invariance properties are discussed. These methods are based on different techniques of group classification and provide means to determine expressions for…
In this paper, it is shown how a combination of approximate symmetries of a nonlinear wave equation with small dissipations and singularity analysis provides exact analytic solutions. We perform the analysis using the Lie symmetry algebra…
We consider a class of (1+2)-dimensional linear partial differential of Asian options pricing. Special cases have been used to models of financial mathematics. We carry out group classification of a class equations. In particular, the…
In this paper, we explain in more details the modern treatment of the problem of group classification of (systems of) partial differential equations (PDEs) from the algorithmic point of view. More precisely, we revise the classical…
We expand our group classification of quasilinear evolution equations (Acta Appl.Math., v.69, 2001) to the case of general evolution equation in one spatial variable. This enables obtaining several new classes of evolution equations with…