Related papers: Extended lattice Gelfand-Dickey hierarchy
A pedagogical presentation of integrable models with special reference to the Toda lattice hierarchy has been attempted. The example of the KdV equation has been studied in detail, beginning with the infinite conserved quantities and going…
Under three relations connecting the field variables of Toda flows and that of KdV flows, we present three new sequences of combination of the equations in the Toda hierarchy which have the KdV hierarchy as a continuous limit. The relation…
For the Harry Dym hierarchy, a non-standard Lax formulation is deduced from that of Korteweg-de Vries (KdV) equation through a reciprocal transformation. By supersymmetrizing this Lax operator, a new N=2 supersymmetric extension of the…
We consider differential-difference equations that determine the continuous symmetries of discrete equations on the triangular lattice. It is shown that a certain combination of continuous flows can be represented as a scalar evolution…
Based on the matrix-resolvent approach, for an arbitrary solution to the discrete KdV hierarchy, we define the tau-function of the solution, and compare it with another tau-function of the solution defined via reduction of the Toda lattice…
We construct generalized additional symmetries of a two-component BKP hierarchy defined by two pseudo-differential Lax operators. These additional symmetry flows form a Block type algebra with some modified(or additional) terms because of a…
In a capacitated directed graph, it is known that the set of all min-cuts forms a distributive lattice [1], [2]. Here, we describe this lattice as a regular predicate whose forbidden elements can be advanced in constant parallel time after…
We expand the most general lattice Dirac operator D in a basis of simple operators. The Ginsparg-Wilson equation turns into a system of coupled quadratic equations for the expansion coefficients. Our expansion of D allows for a natural…
Hirota's discrete Korteweg-de Vries equation (dKdV) is an integrable partial difference equation on 2-dimensional integer lattice, which approaches the Korteweg-de Vries equation in a continuum limit. We find new transformations to other…
The aim of this paper is to summarize some recently obtained relations between the Ablowitz-Ladik hierarchy (ALH) and other integrable equations. It has been shown that solutions of finite subsystems of the ALH can be used to derive a wide…
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…
Results on the finite nonperiodic Toda lattice are extended to some generalizations of the system: The relativistic Toda lattice, the generalized Toda lattice associated with simple Lie groups and the full Kostant-Toda lattice. The areas…
We study from a Hamiltonian point of view the generalized dispersionless KdV hierarchy of equations. From the so called dispersionless Lax representation of these equations we obtain three compatible Hamiltonian structures. The second and…
In this paper, we have studied the kink and antikink solutions in several neutral scalar models in 1+1 dimension. We follow the standard approach to write down the leading order and the second order force between long distance separated…
It is well-known that the finite-gap solutions of the KdV equation can be generated by its recursion operator.We generalize the result to a special form of Lax pair, from which a method to constrain the integrable system to a…
A method is proposed in this paper to construct a new extended q-deformed KP ($q$-KP) hiearchy and its Lax representation. This new extended $q$-KP hierarchy contains two types of q-deformed KP equation with self-consistent sources, and its…
We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to the discrete AKNS hierarchy and,…
We extend the Sato equations of the N=(1|1) supersymmetric Toda lattice hierarchy by two new infinite series of fermionic flows and demonstrate that the algebra of the flows of the extended hierarchy is the Borel subalgebra of the N=(2|2)…
Under the Neumann constraints, each equation of the KdV hierarchy is decomposed into two finite dimensional systems, including the well-known Neumann model. Like in the case of the Bargmann constraint, the explicit Lax representations are…
A generating function of the single Hurwitz numbers of the Riemann sphere $\mathbb{CP}^1$ is a tau function of the lattice KP hierarchy. The associated Lax operator $L$ turns out to be expressed as $L = e^{\mathfrak{L}}$, where…