arXiv subjects

Ivan Tsyfra

Publications and source records attributed to Ivan Tsyfra.

4 recordsLinked to original sources

arXiv2018

On a reduction of nonlinear evolution and wave type equations via non-point symmetry method

We study the symmetry reduction of nonlinear evolution and wave type differential equations by using operators of non-point symmetry. In our approach we use both operators of classical and conditional symmetry. It appears that the combination of non-point and conditional symmetry enables us to construct not only solutions but Bäcklund transformations too for the equation under study. We show that the method can be applied to nonevolutionary partial differential equations.

math.AP↗

arXiv2017

Non-point symmetry reduction method of partial differential equations

We study the symmetry reduction of nonlinear partial differential equations with two independent variables. We propose new ansätze reducing nonlinear evolution equations to system of ordinary differential equations. The ansätze are constructed by using operators of non-point classical and conditional symmetry. Then we find solution to nonlinear heat equation which can not be obtained in the framework of the classical Lie approach. By using operators of Lie--Bäcklund symmetries we construct the solutions of nonlinear hyperbolic equations depending on arbitrary smooth function of one variable too. We show that the method can be applied to nonevolutionary partial differential equations.

math.AP↗

arXiv2010

Equivalence and integrability of second order linear ODEs

We consider a class of linear ODEs of second order with variable coefficients and construct its Lie algebra of Lie group of equivalence transformations. Further we find invariants and differential invariants of this Lie algebra and by using them we formulate criteria of equivalence of the equations under consideration. These criteria enable us to characterize some classes integrable in quadratures.

math.CA↗

arXiv1998

Symmetry of the Schrödinger equation with variable potential

We study symmetry properties of the Schrödinger equation with the potential as a new dependent variable, i.e., the transformations which do not change the form of the class of equations. We also consider systems of the Schrödinger equations with certain conditions on the potential. In addition we investigate symmetry properties of the equation with convection term. The contact transformations of the Schrödinger equation with potential are obtained.

math-ph↗