Related papers: On some class of differential-difference equations…
A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known…
Using energy methods, we prove some power-law and exponential decay estimates for classical and nonlocal evolutionary equations. The results obtained are framed into a general setting, which comprise, among the others, equations involving…
The aim of this note is to provide a self-contained classification of the irreducible representations of generalised Kac--Paljutkin Hopf algebras, recently introduced by the second author.
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
These course note first provide an introduction to secondary characteristic classes and differential cohomology. They continue with a presentation of a stable homotopy theoretic approach to the theory of differential extensions of…
In this work a class of self-adjoint quasilinear third-order evolution equations is determined. Some conservation laws of them are established and a generalization on a self-adjoint class of fourth-order evolution equations is presented.
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
We prove a linear and a nonlinear generalization of the Lax-Milgram theorem. In particular we give sufficient conditions for a real-valued function defined on the product of a reflexive Banach space and a normed space to represent all…
Almost all theories of physics have expressed physical laws by means of differential equations. One can ask: why differential equations? What is special about them? This article addresses these questions and is presented as an inquiry-based…
This paper aims to demonstrate the applicability of the L_2-integral transform to Partial Differential Equations (PDEs). Of special interest is section (6), which contains an application of the L_2-transform to a PDE of exponential squared…
We provide certain compatibility conditions for m-accretive operators such that the adjoint of the sum is given by the closure of the sum of the respective adjoint. We revisit the proof of well-posedness of the abstract class of partial…
A form of the Laplace transform is reviewed as a paradigm for an entire class of fractional functional transforms. Various of its properties are discussed. Such transformations should be useful in application to differential/integral…
We present a short overview of the recent results in the theory of diffusion and wave equations with generalised derivative operators. We give generic examples of such generalised diffusion and wave equations, which include time-fractional,…
Group classification of the generalized complex Ginzburg-Landau equations is presented. An approach to group classification of systems of reaction-diffusion equations with general diffusion matrix is developed.
This note reports on the recent advancements in the search for explicit representation, in classical special functions, of the solutions of the fourth-order ordinary differential equations named Bessel-type, Jacobi-type, Laguerre-type,…
In this paper we study about the existence of solutions of certain kind of non-linear differential and differential-difference equations. We give partial answer to a problem which was asked by chen et al. in [13].
These notes aim to provide a classical approach to solving some conformable differential equations based on prior knowledge of how to solve ordinary differential equations. That is, using the methods of separation of variables, homogeneous…
Initial-boundary value problems for nonlinear dispersive equations of evolution of order $2l+1,\;l\in\mathbb{N}$ with a convective term of the form $u^ku_x,\;k\in\mathbb{N}$ have been considered on intervals $(0,L),\;L\in (0,+\infty)$. The…
Integrable discretisations for a class of coupled (super) nonlinear Schrodinger (NLS) type of equations are presented. The class corresponds to a Lax operator with entries in a Grassmann algebra. Elementary Darboux transformations are…
A potential representation for the subset of traveling solutions of nonlinear dispersive evolution equations is introduced. The procedure involves a reduction of a third order partial differential equation to a first order ordinary…