The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool.
The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Amit K. Roy-Chowdhury (University of California, Riverside, USA) (Author)
Inhaltsangabe
INTRODUCTION Lax Equation and IST Conserved Densities and Hamiltonian Structure Symmetry Aspects Observations LIE ALGEBRA Introduction Structure Constants and Basis of Lie Algebra Lie Groups and Lie Algebra Representation of a Lie Algebra Cartan-Killing Form Roots Space Decomposition Lie Groups: Finite and Infinite Dimensional Loop Groups Virasoro Group Quantum Tori Algebra Kac-Moody Algebra Serre's Approach to Kac-Moody Algebra Gradation Other Infinite Dimensional Lie Algebras PROLONGATION THEORY Introduction Sectioning of Forms The KdV Problem The Method of the Hall Structure Prolongation in (2+1) Dimension Method of Pseudopotentials Prolongation Structure and the Backlund Transformation Constant Coefficient Ideal Connections Morphisms and Prolongation Principal Prolongation Structure Prolongations and Isovectors Vessiot's Approach Observations CO-ADJOINT ORBITS Introduction The Kac-Moody Algebra Integrability Theorem: Adler Kostant Symes Superintegrable Systems Nonlinear Partial Differential Equation Extended AKS Theorem Space-Dependent Integrable Equation The Moment Map Moment Map in Relation to Integrable Nonlinear Equation Co-Adjoint Orbit of the Volterra Group SYMMETRIES OF INTEGRABLE SYSTEMS Introduction Lie Point and Lie Backlund Symmetry Lie Backlund Transformation Some New Ideas in Symmetry Analysis Non-Local Symmetries Observations HAMILTONIAN STRUCTURE Introduction Drinfeld Sokolob Approach The Lie Algebraic Approach Example of Hamiltonian Structure and Reduction Hamiltonian Reduction in (2+1) Dimension Hamiltonian Reduction of Drinfeld and Sokolov Kupershmidt's Approach Gelfand Dikii Formula Trace Identity and Hamiltonian Structure Symmetry and Hamiltonian Structure CLASSICAL r-MATRIX Introduction Double Lie Algebra Classical r-Matrix The Use of r-Matrix The r-Matrix and KP Equation
INTRODUCTION Lax Equation and IST Conserved Densities and Hamiltonian Structure Symmetry Aspects Observations LIE ALGEBRA Introduction Structure Constants and Basis of Lie Algebra Lie Groups and Lie Algebra Representation of a Lie Algebra Cartan-Killing Form Roots Space Decomposition Lie Groups: Finite and Infinite Dimensional Loop Groups Virasoro Group Quantum Tori Algebra Kac-Moody Algebra Serre's Approach to Kac-Moody Algebra Gradation Other Infinite Dimensional Lie Algebras PROLONGATION THEORY Introduction Sectioning of Forms The KdV Problem The Method of the Hall Structure Prolongation in (2+1) Dimension Method of Pseudopotentials Prolongation Structure and the Backlund Transformation Constant Coefficient Ideal Connections Morphisms and Prolongation Principal Prolongation Structure Prolongations and Isovectors Vessiot's Approach Observations CO-ADJOINT ORBITS Introduction The Kac-Moody Algebra Integrability Theorem: Adler Kostant Symes Superintegrable Systems Nonlinear Partial Differential Equation Extended AKS Theorem Space-Dependent Integrable Equation The Moment Map Moment Map in Relation to Integrable Nonlinear Equation Co-Adjoint Orbit of the Volterra Group SYMMETRIES OF INTEGRABLE SYSTEMS Introduction Lie Point and Lie Backlund Symmetry Lie Backlund Transformation Some New Ideas in Symmetry Analysis Non-Local Symmetries Observations HAMILTONIAN STRUCTURE Introduction Drinfeld Sokolob Approach The Lie Algebraic Approach Example of Hamiltonian Structure and Reduction Hamiltonian Reduction in (2+1) Dimension Hamiltonian Reduction of Drinfeld and Sokolov Kupershmidt's Approach Gelfand Dikii Formula Trace Identity and Hamiltonian Structure Symmetry and Hamiltonian Structure CLASSICAL r-MATRIX Introduction Double Lie Algebra Classical r-Matrix The Use of r-Matrix The r-Matrix and KP Equation
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