Related papers: Desargues maps and their reductions
We show that the 2-matrix string model corresponds to a coupled system of $2+1$-dimensional KP and modified KP ($\KPm$) integrable equations subject to a specific ``symmetry'' constraint. The latter together with the Miura-Konopelchenko map…
We propose a hierarchy of nonlinearly dispersive generalized Korteweg--de Vries (KdV) evolution equations based on a modification of the Lagrangian density whose induced action functional the KdV equation extremizes. It is shown that two…
It is shown that the integrable discrete Schwarzian KP (dSKP) equation which constitutes an algebraic superposition formula associated with, for instance, the Schwarzian KP hierarchy, the classical Darboux transformation and quasi-conformal…
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…
In this paper squared eigenfunction symmetry of the differential-difference modified Kadomtsev-Petviashvili (D$\Delta$mKP) hierarchy and its constraint are considered. Under the constraint, the Lax triplets of the D$\Delta$mKP hierarchy,…
Whitham modulation theory for certain two-dimensional evolution equations of Kadomtsev-Petviashvili (KP) type is presented. Three specific examples are considered in detail: the KP equation, the two-dimensional Benjamin-Ono (2DBO) equation…
The coupled Kadomtsev--Petviashvili system associated with an elliptic curve, proposed by Date, Jimbo and Miwa [J. Phys. Soc. Jpn., 52:766--771, 1983], is reinvestigated within the direct linearisation framework, which provides us with more…
Systems such as fluid flows in channels and pipes or the complex Ginzburg-Landau system, defined over periodic domains, exhibit both continuous symmetries, translational and rotational, as well as discrete symmetries under spatial…
In this paper we study quantum group deformations of the infinite dimensional symmetry algebra of asymptotically AdS spacetimes in three dimensions. Building on previous results in the finite dimensional subalgebras we classify all possible…
This manuscript recounts some of the author's contributions to algebraic and enumerative combinatorics. We have focused on two types of generalizations of bipartite maps, which are bipartite graphs embedded on surfaces. Maps are known to…
This paper studies the dissipative structure of the system of equations that describes the motion of a compressible, isothermal, viscous-capillar fluid of Korteweg type in one space dimension. It is shown that the system satisfies the…
In this paper we study iterative algorithms for finding a common element of the set of fixed points of $\kappa$-strict pseudocontractions or finding a solution of a variational inequality problem for a monotone, Lipschitz continuous…
We introduce a numerical method for general coupled Korteweg-de Vries systems. The scheme is valid for solving Cauchy problems for arbitrary number of equations with arbitrary constant coefficients. The numerical scheme takes its legality…
KdV6 equation can be described as the Kupershmidt deformation of the KdV equation (see 2008, Phys. Lett. A 372: 263). In this paper, starting from the bi-Hamiltonian structure of the discrete integrable system, we propose a generalized…
Some classes of Deformed Special Relativity (DSR) theories are reconsidered within the Hopf algebraic formulation. For this purpose we shall explore a minimal framework of deformed Weyl-Heisenberg algebras provided by a smash product…
Deligne and Mostow investigated period maps on the configuration spaces $M_{0,n}$ of $n$ ordered points on $\mathbb{P}^1$. The images of these maps are open subsets of certain ball quotients. Moreover, they extend to isomorphisms between…
We extend non-invertible duality concepts from one-dimensional systems to two spatial dimensions by constructing a web of non-invertible dualities for lattice models with subsystem symmetries. For the $\mathbb{Z}_2 \times \mathbb{Z}_2$…
In this paper, we construct the multicomponent modified KP hierarchy and its additional symmetries. The additional symmetries constitute an interesting multi-folds quantum torus type Lie algebra. By a reduction, we also construct the…
We review the integration of the KP hierarchy in several non-standard contexts. Specifically, we consider KP in the following associative differential algebras: an algebra equipped with a nilpotent derivation; an algebra of functions…
We investigate reductions of the two-dimensional Dirac equation imposed by the requirement of the existence of a differential operator $D_n$ of order $n$ mapping its eigenfunctions to adjoint eigenfunctions. For first order operators these…