Titlebook: Symmetries and Differential Equations; George W. Bluman,Sukeyuki Kumei Book 19891st edition Springer Science+Business Media New York 1989

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Potential Symmetries,n differential equations from point symmetries to contact symmetries, and, still more generally, to Lie-Bäklund symmetries, we could find more conservation laws, construct mappings to related differential equations, and determine more invariant solutions.

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Lie Groups of Transformations and Infinitesimal Transformations,ties (1.88), the induced scaling transformations of all quantities (1.88), (1.89), and the induced scaling transformations preserving all constants (1.88), (1.91), are all examples of Lie groups of transformations. Scaling transformations are easily described in terms of their global properties as s

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Potential Symmetries, of the differential equation. In previous chapters we considered symmetries defined by infinitesimal transformations whose infinitesimals depend on independent variables, dependent variables, and derivatives of dependent variables. Such symmetries are . since at any point . the infinitesimals are d

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George W. Bluman,Sukeyuki Kumeirst (1982) and second (1990) editions. The previous texts have been so comprehensive that it is dif?cult to imagine he could add more information to the existing chapters and create additional new chapters. One of the new chapters concerns the multiply-injured child, who presents an increasing probl