Related papers: Integrability Tests for Nonlinear Evolution Equati…
Nonlinear filtering is a pivotal problem that has attracted significant attention from mathematicians, statisticians, engineers, and various other scientific disciplines. The solution to this problem is governed by the so-called filtering…
Integrable difference equations commonly have more low-order conservation laws than occur for nonintegrable difference equations of similar complexity. We use this empirical observation to sift a large class of difference equations, in…
We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…
We present a new method for constructing solutions to nonlinear evolutionary equations describing the propagation and interaction of nonlinear waves.
We describe a recent progress in finding solutions to three-particle evolution equations at leading order in the QCD coupling constant for multiparton correlation functions based on the integrability of corresponding interaction…
We develop a variational technique for some wide classes of nonlinear evolutions. The novelty here is that we derive the main information directly from the corresponding Euler-Lagrange equations. In particular, we prove that not only the…
Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…
We consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal…
We extend existence and uniqueness results of [4] for nonlinear integro-differential equations of Volterra type between real locally complete vector spaces
Invariant and equivariant models incorporate the symmetry of an object to be estimated (here non-parametric regression functions $f : \mathcal{X} \rightarrow \mathbb{R}$). These models perform better (with respect to $L^2$ loss) and are…
The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…
We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…
The objective of this manuscript is to enquire for the solvability of a specific type of non-linear quadratic integral equations via the interesting notion of measure of non-compactness. Firstly, we inquire into couple of exciting fixed…
We conjecture an integrability and linearizability test for dispersive Z^2-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscale expansion give a partial differential equation…
We prove that, for $m\ge 7$, scalar evolution equations of the form $u_t=F(x,t,u,...,u_m)$ which admit a nontrivial conserved density of order $m+1$ are linear in $u_m$. The existence of such conserved densities is a necesary condition for…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
In this paper are examined general classes of linear and non-linear analytical systems of partial differential equations. Indeed the integrability conditions are found and if they are satisfied, the solutions are given as functional series…
In the present paper we consider a general family of two dimensional wave equations which represents a great variety of linear and nonlinear equations within the framework of the transformations of equivalence groups. We have investigated…