Displaying similar documents to “Lie symmetry of a class of nonlinear boundary value problems with free boundaries”

Applications of Lie Group Analysis to Mathematical Modelling in Natural Sciences

N. H. Ibragimov, R. N. Ibragimov (2012)

Mathematical Modelling of Natural Phenomena

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Today engineering and science researchers routinely confront problems in mathematical modeling involving solutions techniques for differential equations. Sometimes these solutions can be obtained analytically by numerous traditional ad hoc methods appropriate for integrating particular types of equations. More often, however, the solutions cannot be obtained by these methods, in spite of the fact that, e.g. over 400 types of integrable second-order ordinary differential equations were...

Lie systems: theory, generalisations, and applications

J. F. Cariñena, J. de Lucas

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Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of mathematics and physics. These facts, together with the authors' recent findings...

Lie commutators in a free diassociative algebra

A.S. Dzhumadil'daev, N.A. Ismailov, A.T. Orazgaliyev (2020)

Communications in Mathematics

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We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.