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KP or mKP: Noncommutative Mathematics of Lagrangian, Hamiltonian, and Integrable Systems

About this Title

Boris A. Kupershmidt, University of Tennessee Space Institute, Tullahoma, TN

Publication: Mathematical Surveys and Monographs
Publication Year: 2000; Volume 78
ISBNs: 978-0-8218-1400-0 (print); 978-1-4704-1305-7 (online)
DOI: https://doi.org/10.1090/surv/078
MathSciNet review: MR1752088
MSC: Primary 37K10; Secondary 35Q58, 37K60

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Table of Contents

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Front/Back Matter

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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