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KP or mKP: Noncommutative Mathematics of Lagrangian, Hamiltonian, and Integrable Systems
 
Boris A. Kupershmidt University of Tennessee Space Institute, Tullahoma, TN
Front Cover for KP or mKP
Available Formats:
Hardcover ISBN: 978-0-8218-1400-0
Product Code: SURV/78
600 pp 
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
Electronic ISBN: 978-1-4704-1305-7
Product Code: SURV/78.E
600 pp 
List Price: $126.00
MAA Member Price: $113.40
AMS Member Price: $100.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $193.50
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  • Back Cover for KP or mKP
KP or mKP: Noncommutative Mathematics of Lagrangian, Hamiltonian, and Integrable Systems
Boris A. Kupershmidt University of Tennessee Space Institute, Tullahoma, TN
Available Formats:
Hardcover ISBN:  978-0-8218-1400-0
Product Code:  SURV/78
600 pp 
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
Electronic ISBN:  978-1-4704-1305-7
Product Code:  SURV/78.E
600 pp 
List Price: $126.00
MAA Member Price: $113.40
AMS Member Price: $100.80
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $193.50
MAA Member Price: $174.15
AMS Member Price: $154.80
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 782000
    MSC: Primary 37; 46; Secondary 35; 49; 58;

    This book develops a theory that can be viewed as a noncommutative counterpart of the following topics: dynamical systems in general and integrable systems in particular; Hamiltonian formalism; variational calculus, both in continuous space and discrete. The text is self-contained and includes a large number of exercises. Many different specific models are analyzed extensively and motivations for the new notions are provided.

    Readership

    Graduate students, research mathematicians, and physicists interested in global analysis and analysis on manifolds.

  • Table of Contents
     
     
    • Chapters
    • 1. The KP hierarchy
    • 2. The MKP hierarchy
    • 3. Between KP and MKP
    • 4. Noncommutative Lagrangian formalism
    • 5. Noncommutative Hamiltonian formalism
    • 6. MKP = M+KP
    • 7. The quasirelativistic KP hierarchy
    • 8. The second construction of integrals of the KP hierarchy
    • 9. KP, then MKP
    • 10. The noncommutative differential-difference calculus
    • 11. The noncommutative Hamiltonian formalism over differential-difference rings
    • 12. Hamiltonian formalism for discrete integrable systems of KP and MKP types
    • 13. The Gibbons forms
    • 14. The hydrodynamical representation
    • 15. Relativistic toda lattice and related systems
    • 16. The idea of Lax representations and its discrete-time analog
    • 17. Systems of the KP type
    • 18. Systems of the MKP type
    • 19. The toda lattice, the relativistic toda lattice, and related systems
  • Reviews
     
     
    • This remarkable book … is written so as to be completely self-contained with most arguments presented in great detail … a remarkable account of a substantial body of work … likely to remain a significant work of reference as the field continues to develop.

      Mathematical Reviews
  • Request Review Copy
  • Get Permissions
Volume: 782000
MSC: Primary 37; 46; Secondary 35; 49; 58;

This book develops a theory that can be viewed as a noncommutative counterpart of the following topics: dynamical systems in general and integrable systems in particular; Hamiltonian formalism; variational calculus, both in continuous space and discrete. The text is self-contained and includes a large number of exercises. Many different specific models are analyzed extensively and motivations for the new notions are provided.

Readership

Graduate students, research mathematicians, and physicists interested in global analysis and analysis on manifolds.

  • Chapters
  • 1. The KP hierarchy
  • 2. The MKP hierarchy
  • 3. Between KP and MKP
  • 4. Noncommutative Lagrangian formalism
  • 5. Noncommutative Hamiltonian formalism
  • 6. MKP = M+KP
  • 7. The quasirelativistic KP hierarchy
  • 8. The second construction of integrals of the KP hierarchy
  • 9. KP, then MKP
  • 10. The noncommutative differential-difference calculus
  • 11. The noncommutative Hamiltonian formalism over differential-difference rings
  • 12. Hamiltonian formalism for discrete integrable systems of KP and MKP types
  • 13. The Gibbons forms
  • 14. The hydrodynamical representation
  • 15. Relativistic toda lattice and related systems
  • 16. The idea of Lax representations and its discrete-time analog
  • 17. Systems of the KP type
  • 18. Systems of the MKP type
  • 19. The toda lattice, the relativistic toda lattice, and related systems
  • This remarkable book … is written so as to be completely self-contained with most arguments presented in great detail … a remarkable account of a substantial body of work … likely to remain a significant work of reference as the field continues to develop.

    Mathematical Reviews
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