Bilinear Integrable Systems: from Classical to Quantum, Continuous to Discrete (eBook)

Proceedings of the NATO Advanced Research Workshop on Bilinear Integrable Systems: From Classical to Quantum, Continuous to Discrete St. Petersburg, Russia, 15-19 September 2002

Ludwig Faddeev, Franklin Lambert, Pierre Van Moerbeke (Herausgeber)

eBook Download: PDF

2007
XVIII, 390 Seiten
Springer Netherlands (Verlag)
978-1-4020-3503-6 (ISBN)

Infos

The CKP hierarchy and the WDVV prepotential.- Quantum invariance groups of particle algebras.- Algebraic Hirota maps.- Boundary states in Susy Sine-Gordon model.- Geometry of discrete integrability. The consistency approach.- Homoclinic orbits and dressing method.- Riemann-Hilbert problem and algebraic curves.- Analytic and algebraic aspects of Toda field theories and their real Hamiltonian forms.- Bilinear avatars of the discrete Painlevé II equation.- Orthogonal polynomials satisfying Q-difference equations.- Discretization of coupled soliton equations.- An adelic W-algebra and rank one bispectral operators.- Toroidal Lie algebra and bilinear identity of the self-dual Yang-Mills hierarchy.- From soliton equations to their zero curvature formulation.- Covariant forms of Lax one-field operators: from Abelian to non-commutative.- On the Dirichlet boundary problem and Hirota equations.- Functional-difference deformations of Darboux-Pöshl-Teller potentials.- Maxwell equations for quantum space-time.- A solvable model of interacting photons.- Discretization of a Sine-Gordon type equation- Hierarchy of quantum explicitly solvable and integrable models.- A two-parameter elliptic extension of the lattice KDV system.- Travelling waves in a perturbed discrete Sine-Gordon equation.- Quantum VS classical Calogero-Moser systems.- Geometrical dynamics of an integrable piecewise-linear mapping.- Free bosons and dispersionless limit of Hirota tau-function.- Similarity reductions of Hirota bilinear equations and Painlevé equations.- On fundamental cycle of periodic Box-Ball systems.- Combinatorics and integrable geometry.- On reductions of some KDV-type systems and their link to the quartic Hénon-Heiles Hamiltonian.- On the bilinear forms of Painlevés 4th equation.

Inhalt

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.

Produkt-Details

• Erscheint lt. Verlag: 16.5.2007
• Reihe/Serie: Nato Science Series II:
• Reihe/Serie: NATO Science Series II: Mathematics, Physics and Chemistry
• Reihe/Serie: NATO Science Series II: Mathematics, Physics and Chemistry
• Zusatzinfo: XVIII, 378 p.
• Verlagsort: Dordrecht
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
• Themenwelt: Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
• Themenwelt: Technik
• Schlagworte: Algebra • Equation • Finite • Function • Geometry • Identity • Lie • Potential
• ISBN-10: 1-4020-3503-9 / 1402035039
• ISBN-13: 978-1-4020-3503-6 / 9781402035036