Related papers: Extended lattice Gelfand-Dickey hierarchy
Geometric interpretation of the Hirota equation is presented as equation describing the Laplace sequence of two-dimensional quadrilateral lattices. Different forms of the equation are given together with their geometric interpretation: (i)…
A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of $\tau$-functions of the Toda lattice…
In this paper, we propose a finite Toda lattice of CKP type (C-Toda) together with a Lax pair. Our motivation is based on the fact that the Camassa-Holm (CH) peakon dynamical system and the finite Toda lattice may be regarded as opposite…
We propose a new second-order accurate lattice Boltzmann formulation for linear elastodynamics that is stable for arbitrary combinations of material parameters under a CFL-like condition. The construction of the numerical scheme uses an…
In this note we present a simple Lax description of the hierarchy of the intermediate long wave equation (ILW hierarchy). Although the linear inverse scattering problem for the ILW equation itself was well known, here we give an explicit…
Birkhoff's representation theorem for finite distributive lattices states that any finite distributive lattice is isomorphic to the lattice of order ideals (lower sets) of the partial order of the join-irreducible elements of the lattice.…
In this article, we focus on extending the notion of lattice linearity to self-stabilizing programs. Lattice linearity allows a node to execute its actions with old information about the state of other nodes and still preserve correctness.…
A new class of lattice Dirac operators $D$ have been recently proposed on the basis of the generalized Ginsparg-Wilson relation, $\gamma_5(\gamma_5 D) + (\gamma_5 D)\gamma_5 =2a^{2k+1}(\gamma_5 D)^{2k+2}$, where $k$ is a non-negative…
We develope a difference calculus analogous to the differential geometry by translating the forms and exterior derivatives to similar expressions with difference operators, and apply the results to fields theory on the lattice [Ref. 1]. Our…
We propose an unconventional formulation of lattice field theories which is quite general, although originally motivated by the quest of exact lattice supersymmetry. Two long standing problems have a solution in this context: 1) Each degree…
We introduce a solvable lattice model for supersymmetric LLT polynomials, also known as super LLT polynomials, based upon particle interactions in super n-ribbon tableaux. Using operators on a Fock space, we prove a Cauchy identity for…
A systematic method of constructing manifestly supersymmetric $1+1$-dimensional KP Lax hierarchies is presented. Closed expressions for the Lax operators in terms of superfield eigenfunctions are obtained. All hierarchy equations being…
We consider complementary dynamical systems related to stationary Korteweg-de Vries hierarchy of equations. A general approach for finding elliptic solutions is given. The solutions are expressed in terms of Novikov polynomials in general…
The Friedrichs extension of minimal linear relation being bounded below and associated with the discrete symplectic system with a special linear dependence on the spectral parameter is characterized by using recessive solutions. This…
In this paper, we continue the study of the Davey-Stewartson system which is one of the most important$(2+1)$ dimensional integrable models. As we showed in the previous paper, the dDS (dispersionless Davey-Stewartson) system arises from…
In this article we give a brief overview of some known results in the theory of obstacle-type problems associated with a class of fourth-order elliptic operators, and we highlight our recent work with collaborators in this direction.…
In the paper, we make use of Manton's analytical method to investigate the force between kink and the anti-kink with large distance in $1+1$ dimensional field theory. The related potential has infinite order corrections of exponential…
The duality between a class of the Davey-Stewartson type coupled systems and a class of two-dimensional Toda type lattices is discussed. A new coupled system related to the recently found lattice is presented. A method for eliminating…
We introduce a method of obtaining a higher order extension problem, \'a la Caffarelli-Silvestre, utilizing ideas from renormalization. Moreover, we give an alternative perspective of the recently developed extension problem for the…
We introduce a hierarchy of mutually commuting dynamical systems on a finite number of Laurent series. This hierarchy can be seen as a prolongation of the KP hierarchy, or a ``reduction'' in which the space coordinate is identified with an…