Related papers: Zero curvature representation for a new fifth-orde…
We obtain compatible Hamiltonian and symplectic structure for a new two-component fifth-order integrable system recently found by Mikhailov, Novikov and Wang (arXiv:0712.1972), and show that this system possesses a hereditary recursion…
For the Bakirov system, which is known to possess only one higher-order local generalized symmetry, we explicitly find a zero-curvature representation containing an essential parameter.
This \textquoteleft research-survey' is meant for beginners in the studies of integrable systems. Here we outline some analytical methods for dealing with a class of nonlinear partial differential equations. We pay special attention to…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
In this work we classify the fifth-order integrable symmetrically coup led systems of weight 0 that possess seventh-order symmetry. we obtained 2 new integrable systems that related bi-Hamiltonian formulations are constructed too.
We consider general integrable systems on graphs as discrete flat connections with the values in loop groups. We argue that a certain class of graphs is of a special importance in this respect, namely quad-graphs, the cellular…
In this work we develop some fifth-order integrable coupled systems of weight $0$ and $1$ which possess seventh-order symmetry. We establish four new systems, where in some cases, related recursion operator and bi-Hamiltonian formulations…
The present paper derives systems of partial differential equations that admit a quadratic zero curvature representation for an arbitrary real semisimple Lie algebra. It also determines the general form of Hamilton's principles and…
The method of contact integrable extensions is used to find new zero-curvature representation for Pleba\~nski's second heavenly equation.
We study the Lax integrability of a nonlinear system of two coupled second-order evolution equations introduced by Ibragimov and Shabat. For this system we find a zero-curvature representation with an essential parameter, construct an…
We extend the recent paradigm "Integrability via Geometry" from dimensions 3 and 4 to higher dimensions, relating dispersionless integrability of partial differential equations to curvature constraints of the background geometry. We observe…
We construct a zero curvature formulation, in superspace, for the sTB-B hierarchy which naturally reduces to the zero curvature condition in terms of components, thus solving one of the puzzling features of this model. This analysis,…
We review the developments of a recently proposed approach to study integrable theories in any dimension. The basic idea consists in generalizing the zero curvature representation for two-dimensional integrable models to space-times of…
A counterpart of the Wadati-Konno-Ichikawa (WKI) soliton hierarchy, associated with so(3,R), is presented through the zero curvature formulation. Its spectral matrix is defined by the same linear combination of basis vectors as the WKI one,…
In this paper we present a local description for complete minimal hypersurfaces in $\mathbb{S}^5$ with zero Gauss-Kronecker curvature, zero $3$-mean curvature and nowhere zero second fundamental form.
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each…
The algebraic structure of the integrable mixed mKdV/sinh-Gordon model is discussed and \textit{}extended to the AKNS/Lund-Regge model and to its corresponding supersymmetric versions. The integrability of the models is guaranteed from the…
We present a criterion of reducibility of a zero curvature representation to a solvable subalgebra, hence to a chain of conservation laws. Namely, we show that reducibility is equivalent to the existence of a section of the generalized…
We generalize the Drinfeld-Sokolov formalism of bosonic integrable hierarchies to superspace, in a way which systematically leads to the zero curvature formulation for the supersymmetric integrable systems starting from the Lax equation in…
We discuss a family of integrable systems on the sphere $S^2$ with an additional integral of third order in momenta. This family contains the Coryachev-Chaplygin top, the Goryachev system, the system recently discovered by Dullin and…