Related papers: Sur les integrales de mouvement du systeme de sinu…
We compute the local integrals of motions of the classical limit of the lattice sine-Gordon system, using a geometrical interpretation of the local sine-Gordon variables. Using an analogous description of the screened local variables, we…
Using the algebraic method of Gardner's deformations for completely integrable systems, we construct the recurrence relations for densities of the Hamiltonians for the Boussinesq and the Kaup-Boussinesq equations. By extending the Magri…
The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the…
In this paper we continue the program, initiated in Ref. hep-th/0112246, to investigate an integrable noncommutative version of the sine-Gordon model. We discuss the origin of the extra constraint which the field function has to satisfy in…
The aim of this note is to present simple proofs of the completeness of Manakov's integrals for a motion of a rigid body fixed at a point in $\mathbb R^n$, as well as for geodesic flows on a class of homogeneous spaces…
In this paper we consider the integrability of the mappings derived from the double discrete related sine-Gordon $(\Delta \Delta RsG)$ equation, which we recently introduced in the paper Higher dimensional integrable mappings, under an…
This work deals with a new family of models, which includes the sine-Gordon model and the double-sine-Gordon, triple-sine-Gordon and so on. The investigation is based on a deformation procedure, which is used to deform a well-known model,…
The inverse scattering theory for the sine-Gordon equation discretized in space and both in space and time is considered.
Using normal coordinate expansions we derive by purely superspace methods the density formula giving the component action corresponding to a superspace supergravity-matter action.
We prove a Morse index theorem for action functionals on paths that are allowed to reflect at a hypersurface (either in the interior or at the boundary of a manifold). Both fixed and periodic boundary conditions are treated.
A covariant field theoretical approach to deep inelastic scattering on the deuteron is presented. The deuteron structure function is calculated in terms of the Bethe-Salpeter amplitude. Numerical calculations for the nucleon contribution…
We consider the sine-Gordon equation on metric graphs with simple topologies and derive vertex boundary conditions from the fundamental conservation laws, such as energy and current conservation. Traveling wave solutions for star and tree…
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…
An integral representation for form-factors of exponential fields in the sine-Gordon model is proposed.
We apply an integral formula obtained by the author for a general $G$--structure to the case of $G=G_2$. We derive an integral formula relating curvatures and some quadratic invariants of the endomorphism induced by the intrinsic torsion.…
We investigate the effect of the breaking of integrability in the integrals of motion of a sine-Gordon-like system. The class of quasi-integrable models, discussed in the literature, inherits some of the integrable properties they are…
This work deals with the presence of defect structures in generalized sine-Gordon models. The models are described by periodic potentials, with substructure having one, two, three or more distinct topological sectors, with multiplicity one,…
We briefly present two-dimensional dilaton gravity from the point of view of integrable systems.
Equations of motion of spinning density for extended objects, and corresponding deviation equations are derived. The problem of motion for a variable mass to a spinning extended object is obtained. Spinning fluids may be considered as a…
This is an expository article for Elsevier's Encyclopedia of Mathematical Physics on the subject in the title. Comments/corrections welcome.