Related papers: On a class of multidimensional integrable hierarch…
We describe a variant of the dressing method giving alternative representation of multidimensional nonlinear PDE as a system of Integro-Differential Equations (IDEs) for spectral and dressing functions. In particular, it becomes single…
We obtain via B\"acklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended…
An isospectral hierarchy of commutative integrable systems associated with a polynomial spectral problem is proposed. The resulting hierarchy possesses a recursion structure controlled by a hereditary operator. The nonisospectral flows…
A countable class of integrable dynamical systems, with four dimensional phase space and conserved quantities in involution (H\_n,I\_n) are exhibited. For $n=1$ we recover Neumann sytem on T*S^2. All these systems are also integrable at the…
We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear…
In this paper, by considering two non-isospectral problems with matrices chosen on the color Lie algebra $\mathfrak{sp}_{1}(6)$, we construct (1+1)-dimensional and (2+1)-dimensional super integrable systems on $\mathfrak{sp}_{1}(6)$.…
Integrable equations in ($1 + 1$) dimensions have their own higher order integrable equations, like the KdV, mKdV and NLS hierarchies etc. In this paper we consider whether integrable equations in ($2 + 1$) dimensions have also the…
Unifying hierarchies of integrable equations are discussed. They are constructed via generalized Hirota identity. It is shown that the Combescure transformations, known for a long time for the Darboux system and having a simple geometrical…
We introduce a novel systematic construction for integrable (3+1)-dimensional dispersionless systems using nonisospectral Lax pairs that involve contact vector fields. In particular, we present new large classes of (3+1)-dimensional…
We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential $m$-form $\Omega_m$ with the coefficients satisfying the Pl\"ucker relations, which is gauge-invariantly closed and its…
In the present paper we introduce a multi-dimensional version of the R-matrix approach to the construction of integrable hierarchies. Applying this method to the case of the Lie algebra of functions with respect to the contact bracket, we…
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized…
A comparison is made between bispectral systems and dual isomonodromic deformation equations. A number of examples are given, showing how bispectral systems may be embedded into isomonodromic ones. Sufficiency conditions are given for the…
Dressing technique is used to construct commuting Lax operators which provide an integrable (canonical) structure behind Witten--Dijkgraaf--Verlinde--Verlinde equations. The commuting flows are related to the isomonodromic flows. Examples…
We consider integrability structures of the generalized Hunter--Saxton equation. In particular, we obtain the Lax representation with nonremovable spectral parameter, find local recursion operators for symmetries and cosymmetries, generate…
An integrable extension of the well known nonlinear Schroedinger (NLS) equation to a higher space-dimension, recently proposed by us, is investigated, exploring its various important aspects. Focusing on the idea of construction its…
Generalized Weierstrass representations for generic surfaces conformally immersed into four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are presented. Integrable deformations of surfaces in these spaces…
The article considers lattices of the two-dimensional Toda type, which can be interpreted as dressing chains for spatially two-dimensional generalizations of equations of the class of nonlinear Schr\"odinger equations. The well-known…
The discrete Lax operators with the spectral parameter on an algebraic curve are defined. A hierarchy of commuting flows on the space of such operators is constructed. It is shown that these flows are linearized by the spectral transform…
A universal integrable hierarchy underlying topological Landau-Ginzburg models of D-tye is presented. Like the dispersionless Toda hierarchy, the new hierarchy has two distinct (``positive" and ``negative") set of flows. Special solutions…