相关论文: Strongly Nonlinear Differential Equations with Car…
By using coupling arguments, Harnack type inequalities are established for a class of stochastic (functional) differential equations with multiplicative noises and non-Lipschitzian coefficients. To construct the required couplings, two…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
The factorisation method commonly used in linear supersymmetric quantum mechanics is extended, such that it can be applied to nonlinear quantum mechanical systems. The new method is distinguishable from the linear formalism, as the…
In this paper, we study nonlinear differential equations satisfied by the generating function of Boole numbers. In addition, we derive some explicit and new interesting identities involving Boole numbers and higher-order numbers arising…
We review a recently-discovered link between the functional relations approach to integrable quantum field theories and the properties of certain ordinary differential equations in the complex domain.
In many nonlinear field theories, relevant solutions may be found by reducing the order of the original Euler-Lagrange equations, e.g., to first order equations (Bogomolnyi equations, self-duality equations, etc.). Here we generalise,…
In this work we derive a functional equation in terms of the Hurwitz-Lerch zeta function along with definite integrals in terms of the incomplete gamma and Hurwitz-Lerch zeta functions. The method used in these derivations is contour…
We develop the basic formalism of complex $q$-analysis to study the solutions of second order $q$-difference equations which reduce, in the $q\rightarrow 1$ limit, to the ordinary Laplace equation in Euclidean and Minkowski space. After…
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…
In this paper, we investigate meromorphic solutions of certain nonlinear partial differential equations in several complex variables involving differential and functional operators. Let $f$ be a non-constant meromorphic function in…
We study differential equations, describing interaction of electromagnetic field with moving sidebars and surfaces, coming from integral electrodynamics laws. It is shown that differential equations contain but the such features of…
Nonlinear perturbation of Fuchsian systems are studied in regions including two singularities. Such systems are not necessarily analytically equivalent to their linear part (they are not linearizable). Nevertheless, it is shown that in the…
We discuss the functional lazy techniques in generation and handling of arbitrarily long sequences of derivatives of numerical expressions in one ``variable''; the domain to which the paper belongs is usually nicknamed ``Automatic…
A non-Archimedean antiderivational line analog of the Cauchy-type line integration is defined and investigated over local fields. Classes of non-Archimedean holomorphic functions are defined and studied. Residues of functions are studied,…
The aim of the paper is twofold. First, we introduce analogs of (partial) derivatives on certain Noncommutative algebras, including some enveloping algebras and their "braided counterparts", namely, the so-called modified Reflection…
We establish a series of integral formulae involving the Hurwitz zeta function. Applications are given to integrals of Bernoulli polynomials, log Gamma(q) and log sin(q).
Planar functions are mappings from a finite field $\mathbb{F}_q$ to itself with an extremal differential property. Such functions give rise to finite projective planes and other combinatorial objects. There is a subtle difference between…
In this paper we study the Neumann problem for a type of fully nonlinear second order elliptic partial differential equations on domains in $\mathbb{C}^{n}$ without any curvature assumptions on the domain.
In this paper we consider the Schr{\"o}dinger equation with nonlinear derivative term. Our goal is to initiate the study of this equation with non vanishing boundary conditions. We obtain the local well posedness for the Cauchy problem on…
Differential equation discovery, a machine learning subfield, is used to develop interpretable models, particularly in nature-related applications. By expertly incorporating the general parametric form of the equation of motion and…