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Realizations of real low-dimensional Lie algebras
Using a new powerful technique based on the notion of megaideal, we construct a complete set of inequivalent realizations of real Lie algebras of dimension no greater than four in vector fields on aExpand
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Admissible Transformations and Normalized Classes of Nonlinear Schrödinger Equations
The theory of group classification of differential equations is analyzed, substantially extended and enhanced based on the new notions of conditional equivalence group and normalized class ofExpand
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New results on group classification of nonlinear diffusion–convection equations
Using a new method and additional (conditional and partial) equivalence transformations, we performed group classification in a class of variable coefficient (1 + 1)-dimensional nonlinearExpand
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Point symmetry group of the barotropic vorticity equation
The complete point symmetry group of the barotropic vorticity equation on the $\beta$-plane is computed using the direct method supplemented with two different techniques. The first technique isExpand
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Singular reduction operators in two dimensions
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. AllExpand
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Enhanced Group Analysis and Exact Solutions of Variable Coefficient Semilinear Diffusion Equations with a Power Source
A new approach to group classification problems and more general investigations on transformational properties of classes of differential equations is proposed. It is based on mappings betweenExpand
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Exact solutions of a remarkable fin equation
TLDR
A model ‘remarkable’ fin equation is singled out from a class of nonlinear ( 1 + 1 ) -dimensional fin equations. Expand
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Algebraic method for finding equivalence groups
The algebraic method for computing the complete point symmetry group of a system of differential equations is extended to finding the complete equivalence group of a class of such systems. TheExpand
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Group analysis of nonlinear fin equations
TLDR
Group classification of a class of nonlinear fin equations is carried out exhaustively. Expand
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Complete point symmetry group of vorticity equation on rotating sphere
The complete point symmetry group of the barotropic vorticity equation on the sphere is determined. The method we use relies on the invariance of megaideals of the maximal Lie invariance algebra of aExpand
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