Lie algebraic methods in integrable systems. (2020)
- Record Type:
- Book
- Title:
- Lie algebraic methods in integrable systems. (2020)
- Main Title:
- Lie algebraic methods in integrable systems
- Further Information:
- Note: Amit K. Roy-Chowdhury.
- Authors:
- Roy-Chowdhury, Amit K
- Contents:
- 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 LieINTRODUCTION; 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 … (more)
- Edition:
- 1st
- Publisher Details:
- Boca Raton : Chapman & Hall/CRC
- Publication Date:
- 2020
- Extent:
- 1 online resource
- Subjects:
- 515.39
Hamiltonian systems
Lie algebras - Languages:
- English
- ISBNs:
- 9781000153330
- Related ISBNs:
- 9781000116786
9781003071785 - Notes:
- Note: Description based on CIP data; resource not viewed.
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- Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
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- Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.
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- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library HMNTS - ELD.DS.583450
- Ingest File:
- 04_041.xml