Titlebook: Applications of Lie Groups to Differential Equations; Peter J. Olver Textbook 1993Latest edition Springer-Verlag New York, Inc. 1993 CON_D

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Introduction to Lie Groups,ncepts and how they can be related. Groups arise as an algebraic abstraction of the notion of symmetry; an important example is the group of rotations in the plane or three-dimensional space. Manifolds, which form the fundamental objects in the field of differential geometry, generalize the familiar

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Symmetry Groups and Conservation Laws,s of conservation of energy, conservation of momentum and so on, plays an important role in the analysis of basic properties of the solutions. In 1918, Emmy Noether proved the remarkable result that for systems arising from a variational principle, every conservation law of the system comes from a c

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Generalized Symmetries,“geometrically” on the space of independent and dependent variables. E. Noether was the first to recognize that one could significantly extend the application of symmetry group methods by including derivatives of the relevant dependent variables in the transformations (or, more correctly, their infi

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Group-Invariant Solutions,ly states that the solutions which are invariant under a given .-parameter symmetry group of the system can all be found by solving a system of differential equations involving . fewer independent variables than the original system. In particular, if the number of parameters is one less than the num

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