Related papers: Functional representation of the Volterra hierarch…
This paper is devoted to the negative flows of the AKNS hierarchy. The main result of this work is the functional representation of the extended AKNS hierarchy, composed of both positive (classical) and negative flows. We derive a finite…
In this paper we introduce the new class of generalized Volterra functions. We prove some integral representations for them via Fox-Wright H-functions and Meijer G-functions. From positivity conditions on the weight in these…
The paper focuses on solving one class of Volterra equations of the first kind, which is characterized by the variability of all integration limits. These equations were introduced in connection with the problem of identifying nonsymmetric…
The aim of this work is to present, in self-contained form, results concerning fundamental and the most important questions related to linear stochastic Volterra equations of convolution type. The paper is devoted to study the existence and…
From a 'discrete' functional zero curvature equation, functional representations of (matrix) Burgers and potential KP (pKP) hierarchies (and others), as well as corresponding Backlund transformations, can be obtained in a surprisingly…
This paper provides a numerical approach for solving the linear stochastic Volterra integral equation using Walsh function approximation and the corresponding operational matrix of integration. A convergence analysis and error analysis of…
The Backlund transformations for the Nizhnik-Novikov-Veselov equation are presented. It is shown that these transformations can be iterated and that the resulting sequence can be described by the Volterra equations. The relationships…
In this article, by means of considering an isospectral operator equation which corresponds to the Volterra lattice, and constructing opportune time evolution problems with negative powers of spectral parameter, and using discrete zero…
The derivation of the Backlund transformations (BTs) is a standard problem of the theory of the integrable systems. Here, I discuss the equations describing the BTs for the Ablowitz-Ladik hierarchy (ALH), which have been already obtained by…
The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application…
Many problems of applied mathematics are reduced to the solution of integral equations with special functions in kernels, therefore the inversion formulas for such equations play an important role in solving boundary value problems for…
An integral equation is a way to encapsulate the relationships between a function and its integrals. We develop a systematic way of describing Volterra integral equations -- specifically an algorithm that reduces any separable Volterra…
The article is devoted to investigation of applications of infinite systems of functional equations for modeling of functions with complicated local structure, that are defined in terms of the nega-$\tilde Q$-representation. The infinite…
In this paper, stochastic Volterra equations driven by cylindrical Wiener process in Hilbert space are investigated. Sufficient conditions for existence of strong solutions are given. The key role is played by convergence of $\alpha$-times…
This paper adopts a highly effective numerical approach for approximating non-linear stochastic Volterra integral equations (NLSVIEs) based on the operational matrices of the Walsh function and the collocation method. The method transforms…
The present paper plans to examine the existence, uniqueness and data dependence of the solution of the fractional functional differential equation with the abstract operator of Volterra, in the context of the Picard operators. We present…
In this paper, we systematically investigate the multidimensional $Z$-transform of functions with values in sequentially complete locally convex spaces over the field of complex numbers. We provide many structural characterizations, remarks…
An extension of the super Korteweg-de Vries integrable system in terms of operator valued functions is obtained. In particular the extension contains the $N=1$ Super KdV and coupled systems with functions valued on a symplectic space. We…
We consider a linear Volterra integral equation of the second kind with a sum kernel $K(t',t)=\sum_i K_i(t',t)$ and give the solution of the equation in terms of solutions of the separate equations with kernels $K_i$, provided these exist.…
We present two hierarchies of partial differential equations in $2+1$ dimensions. Since there exist reciprocal transformations that connect these hierarchies to the Calogero-Bogoyavlenski-Schiff equation and its modified version, we can…