Related papers: The CKP hierarchy and the WDVV prepotential
We consider the problem of uniform interpolation of functions with values in a complex inner product space of finite dimension. This problem can be casted within a modified weighted pluripotential theoretic framework. Indeed, in the…
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…
We discuss the associativity or WDVV equations and demonstrate that they can be rewritten as certain functional relations between the {\it second} derivatives of a single function, similar to the dispersionless Hirota equations. The…
We describe three different approaches to the extended (N=2) supersymmetrization of the multicomponent KP hierarchy. In the first one we utilize only superfermions while in the second only superbosons and in the third superbosons as well as…
In probability and statistics, copulas play important roles theoretically as well as to address a wide range of problems in various application areas. We introduce the concept of multivariate discrete copulas, discuss their equivalence to…
A collection of miscellaneous continuous, semi-discrete, and discrete integrable systems can be associated with each integrable evolution equation of the KdV type. We give them for the Schwarz-KdV equation and generalize to the vector case.…
We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra $H_k(\mathbb Z_m)$. This hierarchy depends on $m$ parameters (one of which can be eliminated), with the usual KP hierarchy…
A general structure is developed from which a system of integrable partial difference equations is derived generalising the lattice KdV equation. The construction is based on an infinite matrix scheme with as key ingredient a (formal)…
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
The paper is devoted to further development of the new approach in equilibrium statistical mechanics the basis of which was worked out in a series of articles by the author. The approach proceeds on the use of a hierarchy of equations for…
A $\bar{\partial}$-formalism for studying dispersionless integrable hierarchies is applied to the dKP hierarchy. Connections with the theory of quasiconformal mappings on the plane are described and some clases of explicit solutions of the…
Using the dbar-problem and dual dbar-problem, we derive bilinear relations which allows us to construct integrable hierarchies in different parametrizations, their Darboux-B\"{a}cklund transformations and to analyze constraints for them ina…
We study multiplicative Diophantine approximation property of vectors and compute Diophantine exponents of hyperplanes via dynamics.
In this paper, we proposed an procedure to construct the completion of the integrable system by adding a perturbation to the generalized matrix problem, which can be used to continuous integrable couplings, discrete integrable couplings and…
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 study the relation between weighted pluripotential on a compact set E in C^N and the pluripotential theory of an associated circed set Z in C^(N+1)
We outline the construction of differential invariants for higher--rank tensors.
In this paper we introduce the classical and quantum covariant Weil algebras. Covariant Weil algebras are simultaneous generalizations of Weil algebras and family algebras. We will define differentials, Lie derivatives and contractions on…
In this paper, we present two methods to obtain the compositional inverses of AGW-PPs. We improve some known results in this topic.
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…