Titlebook: New Trends in Integrability and Partial Solvability; A. B. Shabat,A. González-López,M. A. Rodríguez Conference proceedings 2004 Springer S

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Yang-Baxter Maps and Matrix Solitons,New examples of the Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) on the Grassmannians, arising from the theory of the matrix KdV equation are discussed. The Lax pairs for these maps are produced using the relations with the inverse scattering problem for the matrix Schrödinger operator

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NATO Science Series II: Mathematics, Physics and Chemistryhttp://image.papertrans.cn/n/image/665963.jpg

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On the Prolongation of a Hierarchy of Hydrodynamic Chains,s of the enlarged hierarchy are derived. Several associated nonlinear integrable models are exhibited. In particular, it is found that the Camassa-Holm equation can be described as a second-order differential reduction of one of the new flows included in the hierarchy.

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Superintegrable Systems in Classical and Quantum Mechanics, integrals of motion than degrees of freedom. Typically, in classical mechanics such systems are characterized by periodic motion, in quantum mechanics their energy levels can be calculated algebraically.

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