Displaying similar documents to “Nonlinear connections on dual Lie algebroids.”

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 symmetry of a class of nonlinear boundary value problems with free boundaries

Roman Cherniha, Sergii Kovalenko (2011)

Banach Center Publications

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A class of (1 + 1)-dimensional nonlinear boundary value problems (BVPs), modeling the process of melting and evaporation of solid materials, is studied by means of the classical Lie symmetry method. A new definition of invariance in Lie's sense for BVP is presented and applied to the class of BVPs in question.