Related papers: An inhomogeneous Lax representation for the Hirota…
In a previous article [N. Delice, F.W. Nijhoff and S. Yoo-Kong, J. Phys. A: Math. Theor. 48(3) (2015), 035206] a novel class of elliptic Lax pairs for integrable lattice equations was introduced. The present article proposes a…
In this article, we study about the solutions of second order linear differential equations by considering several conditions on the coefficients of homogenous linear differential equation and its associated non-homogenous linear…
This paper studies isometric immersions of space forms by means of a hierarchy of finite dimensional integrable systems in Lax form on loop algebras.
We consider a Lax pair found by Xia, Qiao and Zhou for a family of two-component analogues of the Camassa-Holm equation, including an arbitrary function $H$, and show that this apparent freedom can be removed via a combination of a…
In this paper, we introduce the notion of incoherent definite orthogonal and Hermitian spaces, and use their neighboring spaces as a tool for the local study of orthogonal and unitary Shimura varieties. This generalizes earlier work, using…
We present a new approach to construction of recursion operators for multidimensional integrable systems which have a Lax-type representation in terms of a pair of commuting vector fields. It is illustrated by the examples of the…
In this paper, without any assumption on $v$ and under extremely mild assumption $u(x)=O(|x|^{K})$ at $\infty$ for some $K\gg1$ arbitrarily large, we prove classification of solutions to the following conformally invariant system with mixed…
For homogeneous difference equation of the second order we study the analogy of Hartman-Wintner problem on asymptotic integration of fundamental system of solutions as argument tends to infinity.
We have derived a new system of mKdV-type equations which can be related to the affine Lie algebra $A_{5}^{(2)}$. This system of partial differential equations is integrable via the inverse scattering method. It admits a Hamiltonian…
Integrable spin systems possess interesting geometrical and gauge invariance properties and have important applications in applied magnetism and nanophysics. They are also intimately connected to the nonlinear Schr\"odinger family of…
In this paper, we have considered second order non-homogeneous linear differential equations having entire coefficients. We have established conditions ensuring non-existence of finite order solution of such type of differential equations.
We present a family of unitary irreducible representations of SU(2) realized in the plane, in terms of the Laguerre polynomials. These functions are similar to the spherical harmonics defined on the sphere. Relations with an space of square…
Functional relation for commuting quantum transfer matrices of quantum integrable models is identified with classical Hirota's bilinear difference equation. This equation is equivalent to the completely discretized classical 2D Toda lattice…
The Umehara algebra is studied with motivation on the problem of the non-existence of common complex submanifolds. In this paper, we prove some new results in Umehara algebra and obtain some applications. In particular, if a complex…
New boundary conditions for integrable nonlinear lattices of the XXX type, such as the Heisenberg chain and the Toda lattice are presented. These integrable extensions are formulated in terms of a generic XXX Heisenberg magnet interacting…
We give the complete set of irreducible representations of U(SU(2))_q when q is a m-th root of unity. In particular we show that their dimensions are less or equal to m. Some of them are not highest weight representations.
We classify the cosemisimple Hopf algebras whose corepresentation semi-ring is isomorphic to that of GL(2). This leads us to define a new family of Hopf algebras which generalize the quantum similitude group of a non-degenerate bilinear…
A new class of infinite-dimensional Lie algebras given a name of Lax operator algebras, and the related unifying approach to finite-dimensional integrable systems with spectral parameter on a Riemann surface, such as Calogero--Moser and…
The Hirota equation is an integrable higher order nonlinear Schr\"{o}dinger type equation which describes the propagation of ultrashort light pulses in optical fibers. We present a standard Darboux transformation for the Hirota equation and…
This paper reconsiders finite variable reductions of the universal Whitham hierarchy of genus zero in the perspective of dispersionless Hirota equations. In the case of one-variable reduction, dispersionless Hirota equations turn out to be…