Ebook: Multi-Hamiltonian Theory of Dynamical Systems

This is a modern approach to Hamiltonian systems where multi-Hamiltonian systems are presented in book form for the first time. These systems allow a unified treatment of finite, lattice and field systems. Having more than one Hamiltonian formulation in a single coordinate system for a nonlinear system is a property closely related to integrability. Thus, the book presents an algebraic theory of integrable systems. It is written for scientists and graduate students.

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Content:
Front Matter....Pages I-X
Preliminary Considerations....Pages 1-12
Elements of Differential Calculus for Tensor Fields....Pages 13-39
The Theory of Hamiltonian and Bi-Hamiltonian Systems....Pages 41-85
Lax Representations of Multi-Hamiltonian Systems....Pages 87-106
Soliton Particles....Pages 107-134
Multi-Hamiltonian Finite Dimensional Systems....Pages 135-247
Multi-Hamiltonian Lax Dynamics in (1+1)-Dimensions....Pages 249-312
Towards a Multi-Hamiltonian Theory of (2+1)-Dimensional Field Systems....Pages 313-336
Back Matter....Pages 337-350

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Content:
Front Matter....Pages I-X
Preliminary Considerations....Pages 1-12
Elements of Differential Calculus for Tensor Fields....Pages 13-39
The Theory of Hamiltonian and Bi-Hamiltonian Systems....Pages 41-85
Lax Representations of Multi-Hamiltonian Systems....Pages 87-106
Soliton Particles....Pages 107-134
Multi-Hamiltonian Finite Dimensional Systems....Pages 135-247
Multi-Hamiltonian Lax Dynamics in (1+1)-Dimensions....Pages 249-312
Towards a Multi-Hamiltonian Theory of (2+1)-Dimensional Field Systems....Pages 313-336
Back Matter....Pages 337-350
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