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书目名称Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems影响因子(影响力)




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浅滩

calorie

panorama

Representations of complex semisimple Lie groups and their real forms,All the Lie algebras and Lie groups considered in this chapter are finite-dimensional; sometimes without mentioning this specifically we confine ourselves to a reductive Lie group, i.e., to a direct product of a simple group by a 1-dimensional center.

moratorium

Integration of nonlinear dynamical systems associated with finite-dimensional Lie algebras,In this chapter we will explicitly construct general solutions for a number of concrete two-dimensional classical nonlinear systems of the type (3.1.4) associated with finite-dimensional Lie algebras. Moreover, in the cases where the one-dimensional (or parametric) solutions are important in applications we perform the necessary reduction.

monogamy

monogamy

Internal symmetries of integrable dynamical systems, description of all their gradings. Therefore, though we can describe explicitly via the general construction the group element uniquely determining the corresponding solutions we cannot describe in terms of a Lie group or its Lie algebra a compact form of the equations themselves.

buoyant

Background of the theory of Lie algebras and Lie groups and their representations,text which describes a group method for integrating a broad class of nonlinear equations of theoretical and mathematical physics. We refer the reader to excellent monographs in this area of mathematics for a deeper and more detailed knowledge (see, e.g., [12, 27, 35, 36, 51, 95, 99, 101, 112–115]).

BALK

妨碍

Scalar Lax-pairs and soliton solutions of the generalized periodic Toda lattice,ns considerably and, moreover, in principle enables one to perform them. The approach suggested in what follows is invariant with respect to a concrete representation of the algebra of internal symmetries and appeals directly to the properties of the algebra.