Related papers: Some Wadati-Konno-Ichikawa type integrable systems…
We analyze the W_N^l algebras according to their conjectured realization as the second Hamiltonian structure of the integrable hierarchy resulting from the interchange of x and t in the l^{th} flow of the sl(N) KdV hierarchy. The W_4^3…
In this paper, we present a new hierarchy which includes the intermediate long wave (ILW) equation at the lowest order. This hierarchy is thought to be a novel reduction of the 1st modified KP type hierarchy. The framework of our…
In this letter, a new generalized matrix spectral problem of Dirac type associated with the super Lie algebra $\mathcal{B}(0,1)$ is proposed and its corresponding super integrable hierarchy is constructed.
Analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is discussed. It is based on the generalized Hirota identity. This approach allows to represent generalized hierarchies of…
In this paper, we discuss an interaction between complex geometry and integrable systems. Section 1 reviews the classical results on integrable systems. New examples of integrable systems, which have been discovered, are based on the Lax…
For any two arbitrary positive integers `$n$' and `$m$', using the $m$--th KdV hierarchy and the $(n+m)$--th KdV hierarchy as building blocks, we are able to construct another integrable hierarchy (referred to as the $(n,m)$--th KdV…
We solve the analytic integrability problem for diferential systems in the plane whose origin is an isolated singularity and the first homogeneous component is a quadratic Lotka-Volterra type. As an application, we give the analytically…
The purpose of this article is to investigate relations between W-superalgebras and integrable super-Hamiltonian systems. To this end, we introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie superalgebra $g$ and…
We briefly review the Whitham hierarchies and their applications to integrable systems of the Seiberg-Witten type. The simplest example of the N=2 supersymmetric SU(2) pure gauge theory is considered in detail and the corresponding Whitham…
We investigate self-similar solutions of the extended discrete KP hierarchy. It is shown that corresponding ansatzes lead to purely discrete equations with dependence on some number of parameters together with equations governing…
We study an integro-differential equation which generalizes the periodic intermediate long wave (ILW) equation. The kernel of the singular integral involved is an elliptic function written as a second order difference of the Weierstrass…
The Cauchy problem for harmonic maps from Minkowski space with its standard flat metric to a certain non-constant curvature Lorentzian 2-metric is studied. The target manifold is distinguished by the fact that the Euler-Lagrange equation…
Scattering of a plane electromagnetic wave by an anisotropic impedance right-angled concave wedge at skew incidence is analyzed. A closed-form solution is derived by reducing the problem to a symmetric order-2 vector Riemann-Hilbert problem…
Integrable systems are derived from inelastic flows of timelike, spacelike, and null curves in 2- and 3- dimensional Minkowski space. The derivation uses a Lorentzian version of a geometrical moving frame method which is known to yield the…
Based on the well-established theory of discrete conjugate nets in discrete differential geometry, we propose and examine discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type. In…
Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…
We derive a set of bilinear functional equations of Hirota type for the partition functions of the $sl(2)$ related integrable statistical models defined on a random lattice. These equations are obtained as deformations of the Hirota…
It is proved that the system of string equations of the dispersionless 2-Toda hierarchy which arises in the planar limit of the hermitian matrix model also underlies certain processes in Hele-Shaw flows.
Integrable structures arise in general relativity when the spacetime possesses a pair of commuting Killing vectors admitting 2-spaces orthogonal to the group orbits. The physical interpretation of such spacetimes depends on the norm of the…
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 $\mathfrak{sp}_{1}(6)$.…