Related papers: Quasi-Lie schemes for PDEs

We provide a general theoretical framework allowing us to extend the classical Lie theory for partial differential equations to the case of equations of fractional order. We propose a general prolongation formula for the study of Lie…

We investigate numerous structural connections between numerical algorithms for partial differential equations (PDEs) and neural architectures. Our goal is to transfer the rich set of mathematical foundations from the world of PDEs to…

Integrability conditions for Lie systems are related to reduction or transformation processes. We here analyse a geometric method to construct integrability conditions for Riccati equations following these approaches. This approach provides…

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids,…

Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featuring both nonlinear solution and gradient dependence in the…

Mixed-dimensional partial differential equations arise in several physical applications, wherein parts of the domain have extreme aspect ratios. In this case, it is often appealing to model these features as lower-dimensional manifolds…

The problem of identifying the dynamical Lie algebras of finite-level quantum systems subject to external control is considered, with special emphasis on systems that are not completely controllable. In particular, it is shown that the…

E.B. Vinberg's theory of quasi-derivations of algebras is extended to a broader framework of near-derivations. This deepens connections between Poisson geometry and Lie theory. Although basic results apply to arbitrary algebras, our…

We present a framework for constructing a first-order hyperbolic system whose solution approximates that of a desired higher-order evolution equation. Constructions of this kind have received increasing interest in recent years, and are…

This is the second part of a series devoting to the generalizations and applications of common theorems in variational bifurcation theory. Using abstract theorems in the first part we obtain many new bifurcation results for quasi-linear…

This work presents qualitative and numerical results on a system of partial differential equations (PDEs) which models certain fluid-fluid interaction dynamics. This system models a compressible fluid in a domain $\Omega^+ \subset…

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…

For any finitely generated abelian group $Q$, we reduce the problem of classification of $Q$-graded simple Lie algebras over an algebraically closed field of "good" characteristic to the problem of classification of gradings on simple Lie…

The understanding of the large-scale structure formation requires the resolution of coupled nonlinear equations describing the cosmic density and velocity fields. This is a complicated problem that, for the last decade, has been essentially…

Generalizing our earlier work, we construct quasi-particle bases of principal subspaces of standard module $L_{X_l^{(1)}}(k\Lambda_0)$ and generalized Verma module $N_{X_l^{(1)}}(k\Lambda_0)$ at level $k\geq 1$ in the case of affine Lie…

In this paper implicit and explicit exact difference schemes (EDS) for system $\textbf{x}' = A\textbf{x}$ of three linear differential equations with constant coefficients are constructed. Numerical simulations for stiff problem and for…

A new class of completely integrable models is constructed. These models are deformations of the famous integrable and exactly solvable Gaudin models. In contrast with the latter, they are quasi-exactly solvable, i.e. admit the algebraic…

The theory of Wasserstein gradient flows in the space of probability measures has made an enormous progress over the last twenty years. It constitutes a unified and powerful framework in the study of dissipative partial differential…

We apply the semi-discrete method, c.f. \emph{N. Halidias and I.S. Stamatiou (2016), On the numerical solution of some non-linear stochastic differential equations using the semi-discrete method, Computational Methods in Applied…

We give a systematic construction of new quasi-exactly solvable systems via Bethe ansatz and supersymmetric quantum mechanics (SUSYQM). Methods based on the intertwining of supercharges have been extensively used in the literature for…