Hardcover ISBN:  9780821814000 
Product Code:  SURV/78 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413057 
Product Code:  SURV/78.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821814000 
eBook: ISBN:  9781470413057 
Product Code:  SURV/78.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 
Hardcover ISBN:  9780821814000 
Product Code:  SURV/78 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470413057 
Product Code:  SURV/78.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Hardcover ISBN:  9780821814000 
eBook ISBN:  9781470413057 
Product Code:  SURV/78.B 
List Price:  $254.00 $191.50 
MAA Member Price:  $228.60 $172.35 
AMS Member Price:  $203.20 $153.20 

Book DetailsMathematical Surveys and MonographsVolume: 78; 2000; 600 ppMSC: 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 selfcontained and includes a large number of exercises. Many different specific models are analyzed extensively and motivations for the new notions are provided.
ReadershipGraduate 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 differentialdifference calculus

11. The noncommutative Hamiltonian formalism over differentialdifference 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 discretetime 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 selfcontained 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


RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Reviews
 Requests
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 selfcontained and includes a large number of exercises. Many different specific models are analyzed extensively and motivations for the new notions are provided.
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 differentialdifference calculus

11. The noncommutative Hamiltonian formalism over differentialdifference 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 discretetime 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 selfcontained 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