The Sine-Gordon Solitons as a N-Body Problem

Abstract

We consider the N-soliton solutions in the sine-Gordon model as a N-body problem. This leads to a relativistic generalization of the Calogero model first introduced by Ruijsenaars. We show that the fundamental Poisson bracket of the Lax matrix is quadratic, and the $r$-matrix is a dynamical one. This is in contrast to the Calogero model where the fundamental Poisson bracket of the Lax matrix is linear.

10 pages LATEX SPhT-93-072; LPTHE-93-40

References in corpus (4)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• Classical R-matrix structure for the Calogero model
• Affine Solitons: A Relation Between Tau Functions, Dressing and Bäcklund Transformations

Cited by in corpus (54)

• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Quantization of Solitons and the Restricted Sine-Gordon Model
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• $R$-matrices for Elliptic Calogero-Moser Models
• The R-matrix structure of the Euler-Calogero-Moser model
• On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model
• Dynamical $r$-matrices for the Elliptic Calogero-Moser Model
• Towards effective topological gauge theories on spectral curves
• Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
• Rational Top and its Classical R-matrix
• The hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars-Schneider-van Diejen models: Lax matrices and duality
• Affine Toda Solitons and Systems of Calogero-Moser Type
• Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?
• Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are governed by the same r-matrix
• Giant Magnons in AdS4 x CP3: Embeddings, Charges and a Hamiltonian
• On the Two Gap Locus for the Elliptic Calogero--Moser Model
• The Geometrodynamics of Sine-Gordon Solitons
• p,q-Duality and Hamiltonian Flows in the Space of Integrable Systems or Integrable Systems as Canonical Transforms of the Free Ones
• Hidden Virasoro Symmetry of (Soliton Solutions of) the Sine Gordon Theory
• Relativistic Calogero-Sutherland Model: Spin Generalization, Quantum Affine Symmetry and Dynamical Correlation Functions
• Action-angle duality between the C(n)-type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models
• Dynamical Correlation Functions and Finite-size Scaling in Ruijsenaars-Schneider Model
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System
• Quasi-integrable KdV models, towers of infinite number of anomalous charges and soliton collisions
• On complete solution of the quantum Dell system
• Integrable discretizations of the spin Ruijsenaars-Schneider models
• Exact solutions for N-magnon scattering
• Dualities in quantum integrable many-body systems and integrable probabilities -- I
• Exact quantum S-matrices for solitons in simply-laced affine Toda field theories
• Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• New classical integrable systems from generalized $T\bar{T}$-deformations
• Giant Magnons in Symmetric Spaces: Explicit N-soliton solutions for CP^n, SU(n) and S^n
• On the scattering theory of the classical hyperbolic C(n) Sutherland model
• Quantum Trace Formulae for the Integrals of the Hyperbolic Ruijsenaars-Schneider model
• N-body Dynamics of Giant Magnons in RxS2
• The dynamical twisting and nondynamical r-matrix structure of elliptic Ruijsenaars-Schneider model
• Linear r-Matrix Algebra for a Hierarchy of One-Dimensional Particle Systems Separable in Parabolic Coordinates
• Structures in BC_N Ruijsenaars-Schneider models
• Self-dual Hamiltonians as Deformations of Free Systems
• From solitons to many-body systems
• Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)
• $A_n^{(1)}$ Toda solitons and the dressing symmetry
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• A Note on the Symplectic Structure on the Dressing Group in the sinh--Gordon Model
• Classical r-matrix structure for elliptic Ruijsenaars chain and 1+1 field analogue of Ruijsenaars-Schneider model
• On the Algebraic--Geometrical Solutions of the sine--Gordon Equation
• Integrable many-body systems of Calogero-Ruijsenaars type
• Dressing Transformations and the Algebraic--Geometrical Solutions in the Conformal Affine $sl(2)$ Toda Model
• Pseudolocalized Three-Dimensional Solitary Waves as Quasi-Particles
• Quantum Dynamical $\check{R}$- Matrix with Spectral Parameter from Fusion
• Inverse scattering and the symplectic form for sine-Gordon solitons
• Classical dynamical r-matrices for Calogero-Moser systems and their generalizations
• Vertex Operator Representation of the Soliton Tau Functions in the $A_n^{(1)}$ Toda Models by Dressing Transformations