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Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete

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We gathered here in a lovely and quaint fishing port, Marciana Marina on the island of Elba, to celebrate one of the pioneers of integrable systems, Hirota
Sensei, and this at the occasion of his seventieth birthday. Trained as a physicist in his home university Kyushu University, Professor Hirota earned his PhD in ?61 at Northwestern University with Professor Siegert in the field of ?Quantum Statistical mechanics?. He wrote a widely appreciated Doctoral dissertation on ?Functional Integral representation of the grand partition function?. We are also celebrating another birthday, namely the birth, some thirty years ago, of multisoliton solutions for the KdV equation, the representation of in-tegrable equations as bilinear equation and Hirota?s D-operation. All this happened in the period 1971 through 1974.

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The CKP hierarchy and the WDVV prepotential; H. Aratyn, J. van de Leur.- Quantum invariance groups of particle algebras; M. Arik.- Algebraic Hirota maps; C. Athorne.- Boundary states in Susy Sine-Gordon model; Z. Bajnok et al.- Geometry of discrete integrability. The consistency approach; A.I. Bobenko.- Homoclinic orbits and dressing method; E.V. Doktorov, V.M. Rothos.- Riemann-Hilbert problem and algebraic curves; V. Enolskii, T. Grava.- Analytic and algebraic aspects of Toda field theories and their real Hamiltonian forms; V.S. Gerdjikov.- Bilinear avatars of the discrete Painlevé II equation; B. Grammaticos et al.- Orthogonal polynomials satisfying Q-difference equations; L. Haine.- Discretization of coupled soliton equations; R. Hirota.- An adelic W-algebra and rank one bispectral operators; E. Horozov.- Toroidal Lie algebra and bilinear identity of the self-dual Yang-Mills hierarchy; S. Kakei.- From soliton equations to their zero curvature formulation; F. Lambert, J. Springael.- Covariant forms of Lax one-field operators: from Abelian to non-commutative; S. Leble.- On the Dirichlet boundary problem and Hirota equations; A. Marshakov, A. Zabrodin.- Functional-difference deformations of Darboux-Pöshl-Teller potentials; V.B. Matveev.- Maxwell equations for quantum space-time; R.M. Mir-Kasmov.- A solvable model of interacting photons; J. Naudts.- Discretization of a Sine-Gordon type equation; Y. Ohta.- Hierarchy of quantum explicitly solvable and integrable models; A.K. Pogrebkov.- A two-parameter elliptic extension of the lattice KDV system; S.E. Puttock, F.W. Nijhoff.- Travelling waves in a per-turbed discrete Sine-Gordon equation; V.M. Rothos, M. Feckan.- Quantum VS classical Calogero-Moser systems; R. Sasaki.- Geometrical dynamics of an integrable piecewise-linear mapping; D. Takahashi, M. Iwao.- Free bosons and dispersionless limit of Hirota tau-function; L.A. Takhtajan.- Similarity reductions of Hirota bilinear equations and Painlevé equations; K.M.Tamizhmani et al.- On fundamental cycle of periodic Box-Ball systems; T. Tokihiro.- Combinatorics and integrable geometry; P. van Moerbeke.- On reductions of some KDV-type systems and their link to the quartic Hénon-Heiles Hamiltonian; C. Verhoeven et al.- On the bilinear forms of Painlevé’s 4th equation; R. Willox, J. Hietarinta.