Related papers: Quasi-Lie schemes for PDEs
The effective technique for analyzing representation-independent features of quantum systems based on the semiclassical approximation (developed elsewhere), has been successfully used in the context of the canonical (Weyl) algebra of the…
We utilize extreme-learning machines for the prediction of partial differential equations (PDEs). Our method splits the state space into multiple windows that are predicted individually using a single model. Despite requiring only few data…
This paper addresses Bayesian inference related to partial differential equations (PDEs), particularly nonparametric regression constrained by PDEs. To effectively encode prior information, we propose a novel framework that learns a…
Invariants of general linear system of two hyperbolic partial differential equations (PDEs) are derived under transformations of the dependent and independent variables by real infinitesimal method earlier. Here a subclass of the general…
We examine the Lie symmetries of a semi-linear partial differential equations and their connections to the analogous symmetries of the forward-backward stochastic differential equations (FBSDEs), established through the generalized…
Latent variable models are widely used to account for unobserved determinants of economic behavior. This paper introduces a quasi-Bayes approach to nonparametrically estimate a large class of latent variable models. As an application, we…
In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
Polynomial Lie (super)algebras $g_{pd}$ are introduced via $G_{i}$-invariant polynomial Jordan maps in quantum composite models with Hamiltonians $H$ having invariance groups $G_{i}$. Algebras $g_{pd}$ have polynomial structure functions in…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
For linear and fully non-linear diffusion equations of Bellman-Isaacs type, we introduce a class of approximation schemes based on differencing and interpolation. As opposed to classical numerical methods, these schemes work for general…
Using the technique of quasi difference sets we characterize geometry and automorphisms of configurations which can be presented as a join of some others, in particular - which can be presented as series of cyclically inscribed copies of…
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…
We present a contribution to the field of system identification of partial differential equations (PDEs), with emphasis on discerning between competing mathematical models of pattern-forming physics. The motivation comes from developmental…
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered.…
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. In this paper we present a generalization of quasilinear theory to include dynamic mode…
It is shown how traditional development of theories of fluids based upon the concept of physical clustering can be adapted to an alternative local clustering definition. The alternative definition can preserve a detailed valence description…
We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of…
Using the principle of structural analogy of solutions, approaches have been developed for constructing exact solutions of complex nonlinear PDEs, including PDEs with delay, based on the use of special solutions to auxiliary simpler related…
We provide linearizability criteria for a class of systems of third-order ordinary differential equations (ODEs) that is cubically semi-linear in the first derivative, by differentiating a system of second-order quadratically semi-linear…