相关论文: Negative Volterra flows

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…

We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces

We study the negative flows of the hierarchy of the integrable Heisenberg Ferromagnet model and their soliton solutions. The first negative flow is related to the so-called short pulse equation. We provide a framework which generates Lax…

An approach to master symmetries of lattice equations is proposed by the use of discrete zero curvature equation. Its key is to generate non-isospectral flows from the discrete spectral problem associated with a given lattice equation. A…

Modified Volterra lattice admits two vector generalizations. One of them is studied for the first time. The zero curvature representations, B\"acklund transformations, nonlinear superposition principle and the simplest explicit solutions of…

Volterra's integral equations with local and nonlocal loads represent the novel class of integral equations that have attracted considerable attention in recent years. These equations are a generalisation of the classic Volterra integral…

A vector calculus approach for the determination of advected invariants is presented for inviscid fluid flow. This approach describes invariants by means of Lie dragging of scalars, vectors, and skew-tensors with respect to the fluid…

The inverse Laplace transform can turn a linear differential equation on a complex domain into an equivalent Volterra integral equation on a real domain. This can make things simpler: for example, a differential equation with irregular…

Modular flows probe important aspects of the entanglement structures, especially those of QFTs, in a dynamical framework. Despite the expected non-local nature in the general cases, the majority of explicitly understood examples feature…

The existence of continuous not necessarily bounded solutions of nonlinear functional Volterra integral inclusions in infinite dimensional setting is shown with the aid of the measure of nonequicontinuity. New abstract topological fixed…

This work aims to bridge the gap between pure and applied research on scalar, linear Volterra equations by examining five major classes: integral and integro-differential equations with completely monotone kernels, such as linear…

We consider an hierarchy of integrable 1+2-dimensional equations related to Lie algebra of the vector fields on the line. The solutions in quadratures are constructed depending on $n$ arbitrary functions of one argument. The most…

Predicting the conditional evolution of Volterra processes with stochastic volatility is a crucial challenge in mathematical finance. While deep neural network models offer promise in approximating the conditional law of such processes,…

We apply the monotone domain decomposition iterative method to a nonlinear integro-differential equation of Volterra type and prove its convergence. To do this, by adding a term in both sides of the original equation we make a linear…

Some results about existence, uniqueness, and attractive behaviour of solutions for nonlinear Volterra integral equations with non-convolution kernels are presented in this paper. These results are based on similar ones about nonlinear…

We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state…

We carry out the generalization of the Lotka-Volterra embedding to flows not explicitly recognizable under the Generalized Lotka-Volterra format. The procedure introduces appropiate auxiliary variables, and it is shown how, to a great…

This paper aims at building a unified framework to deal with a wide class of local and nonlocal translation-invariant geometric flows. First, we introduce a class of generalized curvatures, and prove the existence and uniqueness for the…

A construction of negative flows for integrable systems based on the Lax representation and squared eigenfunctions is proposed. Examples considered include the Boussinesq equation and its reduction to the Sawada-Kotera and Kaup-Kupershmidt…

The variational iteration method is used to solve nonlinear Volterra integral equations. Two approaches are presented distinguished by the method to compute the Lagrange multiplier.