Related papers: Hierarchy of Higher Dimensional Integrable System

It is well known that integrable hierarchies in (1+1) dimensions are local while the recursion operators that generate them usually contain nonlocal terms. We resolve this apparent discrepancy by providing simple and universal sufficient…

We obtain, in local coordinates, the explicit form of the two-dimensional, super-integrable systems of Matveev and Shevchishin involving cubic integrals. This enables us to determine for which values of the parameters these systems are…

Integrable lattice equations arising in the context of singular manifold equations for scalar, multicomponent KP hierarchies and 2D Toda lattice hierarchy are considered. These equation generate the corresponding continuous hierarchy of…

We display a new integrable perturbation for both N=1 and N=2 superconformal minimal models. These perturbations break supersymmetry explicitly. Their existence was expected on the basis of the classification of integrable perturbations of…

We discuss the integrability of the Berkovits-Siegel open string field equations and derive an infinite set of their non-local (solution-generating) symmetries. The string field equations are embedded in an infinite system of overdetermined…

In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous…

Because of all the known integrable models possess Schwarzian forms with M\"obious transformation invariance, it may be one of the best way to find new integrable models starting from some suitable M\"obious transformation invariant…

The Sine-Gordon equation is integrable in (1+1)-dimensional Minkowski and in 2-dimensional Euclidean spaces. In each case, it has a Lax pair, and a Hirota algorithm generates its N soliton solutions for all N greater than or equal to 1. The…

In this paper we discuss topological BF theories in 3 and 4 dimensions. Observables are associated to ordinary knots and links (in 3 dimensions) and to 2-knots (in 4 dimensions). The vacuum expectation values of such observables give a wide…

In this paper, we continue the study of the Davey-Stewartson system which is one of the most important$(2+1)$ dimensional integrable models. As we showed in the previous paper, the dDS (dispersionless Davey-Stewartson) system arises from…

Using the dbar-problem and dual dbar-problem, we derive bilinear relations which allows us to construct integrable hierarchies in different parametrizations, their Darboux-B\"{a}cklund transformations and to analyze constraints for them ina…

The compressible Navier-Stokes-Poisson system is concerned in the present paper, and the global existence and uniqueness of the strong solution is shown in the framework of hybrid Besov spaces in three and higher dimensions.

We propose a systematic method to generalize the integrable Rosochatius deformations for finite dimensional integrable Hamiltonian systems to integrable Rosochatius deformations for infinite dimensional integrable equations. Infinite number…

It is shown that the Ablowitz-Kaup-Newell-Segur (AKNS) integrable hierarchy can be obtained as the dynamical equations of three-dimensional General Relativity with a negative cosmological constant. This geometrization of the AKNS system is…

We introduce an extension of the \ell-reduced KP hierarchy, which we call the \ell-Bogoyavlensky hierarchy. Bogoyavlensky's 2+1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of \ell=2. We present…

The classification of lattice equations that are integrable in the sense of higher-dimensional consistency is extended by allowing directed edges. We find two cases that are not transformable via the 'admissible transformations' to the…

Determining if an (1+1)-differential-difference equation is integrable or not (in the sense of possessing an infinite number of symmetries) can be reduced to the study of the dependence of the equation on the lattice points, according to…

A mixed symmetric Painleve III - V model which describes a hybrid of both equations is defined and obtained by successive self-similarity and Dirac Lagrange multiplier reductions from an integrable 4-boson hierarchy.

It is shown that one system of coupled KdV equations, found in J. Nonlin. Math. Phys., 1999, Vol.6, Nr.3, 255--262 [arXiv:solv-int/9901005] to possess the Painlev\'e property, is integrable but not new.

Symmetry constraints for (2+1)-dimensional dispersionless integrable equations are considered. It is demonstrated that they naturally lead to systems of hydrodynamic type which arise within the reduction method. One also easily obtaines an…