Titlebook: Applications of Lie Groups to Differential Equations; Peter J. Olver Textbook 19861st edition Springer-Verlag New York Inc. 1986 Applicati

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波動

Textbook 19861st editionons. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory

豐富

善變

Th. Liebisch,A. Sch?nflies,O. Mügge. This basic principle constitutes the first fundamental result in the study of classical or quantum-mechanical systems with prescribed groups of symmetries. Moreover, Noether’s method is the only really systematic procedure for constructing conservation laws for complicated systems of partial differential equations.

AWL

Introduction to Lie Groups,he algebraic methods of group theory and the multi-variable calculus used in analytic geometry. This resulting theory, particularly the powerful infinitesimal techniques, can then be applied to a wide range of physical and mathematical problems.

勤勞

Symmetry Groups and Conservation Laws,. This basic principle constitutes the first fundamental result in the study of classical or quantum-mechanical systems with prescribed groups of symmetries. Moreover, Noether’s method is the only really systematic procedure for constructing conservation laws for complicated systems of partial differential equations.

Cupidity

Th. Liebisch,A. Sch?nflies,O. Müggeit appears that the possession of an infinite number of such symmetries is a characterizing property of “solvable” equations, such as the Korteweg-de Vries equation, which have “soliton” solutions or can be linearized either directly or via inverse scattering.