Group-Theoretical Methods for Integration of Nonlinear Dynamical Systems: Progress in Mathematical Physics, cartea 15
Autor Andrei N. Leznov, Mikhail V. Savelieven Limba Engleză Hardback – 22 apr 1992
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Specificații
ISBN-13: 9783764326159
ISBN-10: 3764326158
Pagini: 290
Ilustrații: XVII, 292 p.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.62 kg
Ediția:1992
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Progress in Mathematical Physics
Locul publicării:Basel, Switzerland
ISBN-10: 3764326158
Pagini: 290
Ilustrații: XVII, 292 p.
Dimensiuni: 155 x 235 x 22 mm
Greutate: 0.62 kg
Ediția:1992
Editura: Birkhäuser Basel
Colecția Birkhäuser
Seria Progress in Mathematical Physics
Locul publicării:Basel, Switzerland
Public țintă
ResearchCuprins
Background of the theory of Lie algebras and Lie groups and their representations.- § 1.1 Lie algebras and Lie groups.- § 1.2 ?-graded Lie algebras and their classification.- § 1.3 sl(2)-subalgebras of Lie algebras.- § 1.4 The structure of representations.- § 1.5 A parametrization of simple Lie groups.- § 1.6 The highest vectors of irreducible representations of semisimple Lie groups.- § 1.7 Superalgebras and superspaces.- Representations of complex semisimple Lie groups and their real forms.- § 2.1 Infinitesimal shift operators on semisimple Lie groups.- § 2.2 Casimir operators and the spectrum of their eigenvalues.- § 2.3 Representations of semisimple Lie groups.- § 2.4 Intertwining operators and the invariant bilinear form.- § 2.5 Harmonic analysis on semisimple Lie groups.- § 2.6 Whittaker vectors.- A general method of integrating two-dimensional nonlinear systems.- § 3.1 General method.- § 3.2 Systems generated by the local part of an arbitrary graded Lie algebra.- § 3.3 Generalization for systems with fermionic fields.- § 3.4 Lax-type representation as a realization of self-duality of cylindrically-symmetric gauge fields.- Integration of nonlinear dynamical systems associated with finite-dimensional Lie algebras.- § 4.1 The generalized (finite nonperiodic) Toda lattice.- § 4.2 Complete integration of the two-dimensionalized system of Lotka-Volterra-type equations (difference KdV) as the Bäcklund transformation of the Toda lattice.- § 4.3 String-type systems (nonabelian versions of the Toda system).- § 4.4 The case of a generic Lie algebra.- § 4.5 Supersymmetric equations.- § 4.6 The formulation of the one-dimensional system (3.2.13) based on the notion of functional algebra.- Internal symmetries of integrable dynamical systems.- § 5.1Lie-Bäcklund transformations. The characteristic algebra and defining equations of exponential systems.- § 5.2 Systems of type (3.2.8), their characteristic algebra and local integrals.- § 5.3 A complete description of Lie-Bäcklund algebras for the diagonal exponential systems of rank 2.- § 5.4 The Lax-type representation of systems (3.2.8) and explicit solution of the corresponding initial value (Cauchy) problem.- § 5.5 The Bäcklund transformation of the exactly integrable systems as a corollary of a contraction of the algebra of their internal symmetry.- § 5.6 Application of the methods of perturbation theory in the search for explicit solutions of exactly integrable systems (the canonical formalism).- § 5.7 Perturbation theory in the Yang-Feldmann formalism.- § 5.8 Methods of perturbation theory in the one-dimensional problem.- § 5.9 Integration of nonlinear systems associated with infinite-dimensional Lie algebras.- Scalar Lax-pairs and soliton solutions of the generalized periodic Toda lattice.- § 6.1 A group-theoretical meaning of the spectral parameter and the equations for the scalar LA-pair.- § 6.2 Soliton solutions of the sine-Gordon equation.- § 6.3 Generalized Bargmann potentials.- § 6.4 Soliton solutions for the vector representation of Ar.- Exactly integrable quantum dynamical systems.- § 7.1 The Hamiltonian (canonical) formalism and the Yang-Feldmann method.- § 7.2 Basics from perturbation theory.- § 7.3 One-dimensional generalized Toda lattice with fixed end-points.- § 7.4 The Liouville equation.- § 7.5 Multicomponent 2-dimensional models. 1.- § 7.6 Multicomponent 2-dimensional models. 2.- Afterword.