Titlebook: Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete; Proceedings of the N Ludwig Faddeev,Pierre Van Moerbeke,Fra

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The Rise and Fall of the Alliance,cted case is given through a quasiclassical tau-function, which satisfies the Hirota equations of the dispersionless Toda hierarchy, following from properties of the Dirichlet Green function.We also outline a possible generalization to the case of multiply connected domains related to the multi support solutions of matrix models.

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Deborah F. Shmueli,Rassem Khamaisied. A is the commutative algebra of functions generated by the unitary irreducible representations of the isometry group of the De Sitter .. Corresponding space-time carries the noncommutative geometry (NG) [1–14]. The Gauge invariance principle consistent with this NG is considered.

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QUANTUM INVARIANCE GROUPS OF PARTICLE ALGEBRAS,c inhomogenous orthogonal quantum group which is the inhomogenous quantum invariance group of the .-dimensional fermion algebra. Another is .(2., .), the bosonic inhomogenous symplectic quantum group which is the inhomogenous quantum invariance group of the .-dimensional boson algebra. Complexificat

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ALGEBRAIC HIROTA MAPS,ralized) Hirota derivatives in the limit of the dimension of the representation becoming infinite and we discuss an application to the theory of -functions associated with hyperelliptic curves of genus 2.

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HOMOCLINIC ORBITS AND DRESSING METHOD,yed to obtain homoclinic solutions for NLS with periodic boundaries. We propose a new method to analytically generate homo-clinic solutions for integrable nonlinear PDEs. This approach resembles the dressing method known in the theory of solitons. The pole positions in the dressing factor are given

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