KP or MKP: Noncommutative Mathematics of Lagrangian, Hamiltonian, and Integrable Systems (Mathematical Surveys and Monographs No. 78)
By: Boris A. Kupershmidt (author)Hardback
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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 in this book.
Continuous space-time: The KP hierarchy The mKP hierarchy Between KP and mKP Noncommutative Lagrangian formalism Noncommutative Hamiltonian informalism mKP = m + KP The quasirelativistic KP hierarchy The second construction of integrals of the KP hierarchy Discrete space-continuous time: KP, then mKP The noncommutative differential-difference calculus The noncommutative Hamiltonian formalism over differential-difference Hamiltonian formalism for discrete integrable systems of KP and mKP types The Gibbons forms The hydrodynamical Ansatz Relativistic Toda lattice and related systems Discrete space-time: The idea of Lax representations and its discrete-time analog Systems of the KP type Systems of mKP type The Toda lattice, the relativistic Toda lattice, and related systems Appendices: Complexification of Hamiltonian systems Asymptotic expansions of Hamiltonian systems Variational calculus over noncommutative rings Hamiltonian correspondencies Covariant aspects of the Hamiltonian formalism Noncommutative solitons The noncommutative KP equation A list of scalar equations Open problems and conjectures Notes and comments Bibliography Index/notations.
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- ID: 9780821814000
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