相关论文: A formula for symmetry recursion operators from no…
We find direct and inverse recursion operators for integrable cases of the rmdKP and rdDym equations. Also, we study actions of these operators on the contact symmetries and find shadows of nonlocal symmetries of these equations.
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
A completely integrable nonlinear partial differential equation (PDE) can be associated with a system of linear PDEs in an auxiliary function whose compatibility requires that the original PDE is satisfied. This associated system is called…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
Let $D$ and $U$ be linear operators in a vector space (or more generally, elements of an associative algebra with a unit). We establish binomial-type identities for $D$ and $U$ assuming that either their commutator $[D,U]$ or the second…
In this paper we devise a systematic procedure to obtain nonlocal symmetries of a class of scalar nonlinear ordinary differential equations (ODEs) of arbitrary order related to linear ODEs through nonlocal relations. The procedure makes use…
We represent an algorithm allowing one to construct new classes of partially integrable multidimensional nonlinear partial differential equations (PDEs) starting with the special type of solutions to the (1+1)-dimensional hierarchy of…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
In this work we develop a general procedure for constructing the recursion operators fro non-linear integrable equations admitting Lax representation. Svereal new examples are given. In particular we find the recursion operators for some…
In this paper, we propose simple numerical algorithms for partial differential equations (PDEs) defined on closed, smooth surfaces (or curves). In particular, we consider PDEs that originate from variational principles defined on the…
In this paper we introduce an observer design framework for ordinary differential equation (ODE) systems based on various types of existing or even novel one-parameter symmetries (exact, asymptotic and variational) ending up with a certain…
We construct, for any given $ \ell = \frac{1}{2} + {\mathbb N}_0, $ the second-order \textit{nonlinear} partial differential equations (PDEs) which are invariant under the transformations generated by the centrally extended conformal…
Reduction operators, i.e. the operators of nonclassical (or conditional) symmetry of a class of variable coefficient nonlinear wave equations with power nonlinearities is investigated within the framework of singular reduction operator. A…
This short note completes the symmetry analysis of a class of quasi-linear partial differential equations considered in the previous paper (Nonlinear Dynamics, Vol. 51, 309-316 (2008)): it deals with the presence of an "exceptional" Lie…
Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…
We introduce a general difference quotient representation for non-local operators associated with a first-order linear operator. We establish new local to non-local estimates and strong localization principles in various spaces of…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Recent advances in the theory of Neural Operators (NOs) have enabled fast and accurate computation of the solutions to complex systems described by partial differential equations (PDEs). Despite their great success, current NO-based…
In this article we present first an algorithm for calculating the determining equations associated with so-called ``nonclassical method'' of symmetry reductions (a la Bluman and Cole) for systems of partial differentail equations. This…
Second-order partial differential equations in non-divergence form are considered. Equations of this kind typically arise as subproblems for the solution of Hamilton-Jacobi-Bellman equations in the context of stochastic optimal control, or…