相关论文: Strongly Nonlinear Differential Equations with Car…

Ordinary and partial differential equation for unknown functions defined on the Cantor dyadic group are studied. We consider two types of equations: related to the Gibbs derivatives and to the fractional modified Gibbs derivatives (or…

The construction of stochastic solutions for nonlinear partial differential equations is a powerful method to obtain new exact results and to develop efficient numerical algorithms, in particular when domain decomposition techniques are…

Several families of nonlinear field equations are known to possess space- localized singularity-free solutions which describe fields with finite Hermitian norms. This paper studies the interaction of such fields with given electromagnetic…

Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…

In this article we investigate the nature of the functions, including important double power terms which arise naturally in considering typical nonlinear Schroedinger equations.

The non-commutative differential calculus on the quantum groups $SL_q(N)$ is constructed. The quantum external algebra proposed contains the same number of generators as in the classical case. The exterior derivative defined in the…

We consider nonhomogeneous fractional $p$-Laplace equations defined on a bounded nonsmooth domain which goes beyond the Lipschitz category. Under a sufficient flatness assumption on the domain in the sense of Reifenberg, we establish…

New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…

The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…

The Cauchy problem for fractional derivatives linear systems of ordinary differential equations with constant coefficients is considered, where at first the analytic expressions are given through the matrix exponent of its corresponding…

We study non-linear differential equations on the punctured formal disc by considering the natural derived enhancements of their spaces of solutions. In particular, by appealing to results of the inverse theory in the calculus of…

Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…

An umbral calculus over local fields of positive characteristic is developed on the basis of a relation of binomial type satisfied by the Carlitz polynomials. Orthonormal bases in the space of continuous $\mathbb F_q$-linear functions are…

A class of self-similar solutions to the derivative nonlinear Schr\"odinger equations is studied. Especially, the asymptotics of profile functions are shown to posses a logarithmic phase correction. This logarithmic phase correction is…

Cauchy and exponential transforms are characterized, and constructed, as canonical holomorphic sections of certain line bundles on the Riemann sphere defined in terms of the Schwarz function. A well known natural connection between Schwarz…

Scalar field systems containing higher derivatives are studied and quantized by Hamiltonian path integral formalism. A new point to previous quantization methods is that field functions and their derivatives with time are considered as…

Nonlinear integrable equations serve as a foundation for nonlinear dynamics, and fractional equations are well known in anomalous diffusion. We connect these two fields by presenting the discovery of a new class of integrable fractional…

Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…

We study a fourth-order derivative scalar field configuration in a fixed Lifshitz background. Using an auxiliary field we rewrite the equations of motion as two coupled second order equations. We specialize to the limit that the mass of the…

Within the framework of mappings between affine spaces, the notion of $n$-th polarization of a function will lead to an intrinsic characterization of polynomial functions. We prove that the characteristic features of derivations, such as…