Related papers: Non-invertible transformations for the classificat…
We develop the approach to the problem of integrable discretization based on the notion of $r$--matrix hierarchies. One of its basic features is the coincidence of Lax matrices of discretized systems with the Lax matrices of the underlying…
The classical Lagrange inversion formula is extended to analytic and non--analytic inversion problems on non--Archimedean fields. We give some applications to the field of formal Laurent series in $n$ variables, where the non--analytic…
Nonlinear integrable models with two spatial and one temporal variables: Kadomtsev-Petviashvili equation and two-dimensional Toda lattice are investigated on the subject of correct formulation for boundary problem that can be solved within…
The five integrable vortex equations, recently studied by Manton, are generalized to include magnetic impurities of the Tong-Wong type. Under certain conditions these generalizations remain integrable. We further set up a gauge theory with…
We investigate the relation between the local variables of a discrete integrable lattice system and the corresponding separation variables, derived from the associated spectral curve. In particular, we have shown how the inverse…
A systematic framework is presented for the construction of hierarchies of soliton equations. This is realised by considering scalar linear integral equations and their representations in terms of infinite matrices, which give rise to all…
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
Transformations of differential equations to other equivalent equations play a central role in many routines for solving intricate equations. A class of differential equations that are particularly amenable to solution techniques based on…
B\"acklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of B\"acklund transformations admitted by this equation are constructed. Schwartzian derivative as well as its invariance…
Physics-informed neural networks have emerged as a prominent new method for solving differential equations. While conceptually straightforward, they often suffer training difficulties that lead to relatively large discretization errors or…
We show that nonlocal reductions of systems of integrable nonlinear partial differential equations are the special discrete symmetry transformations.
We establish a Liouville type theorem for some conformally invariant fully nonlinear equations
We introduce the sub-lattice approach, a procedure to generate, from a given integrable lattice, a sub-lattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point…
In this work, we construct novel discretizations for the unsteady convection-diffusion equation. Our discretization relies on multiderivative time integrators together with a novel discretization that reduces the total number of unknowns…
Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…
We give a definition of finitary type theories that subsumes many examples of dependent type theories, such as variants of Martin-L\"of type theory, simple type theories, first-order and higher-order logics, and homotopy type theory. We…
In this paper we classify irreducible integrable representations of loop toroidal Lie algebras with finite dimensional weight spaces. In both the cases we classify modules, when a part of center acts non-trivially and trivially on modules.
The Lie theory of non-commutative integrability is used to reconstruct some integrable systems of ordinary differential equations in three dimensional Eucledian space. The Darboux-Brioschi-Halphen system is an example of the Lie integrable…
Techniques are developed for decoupling dissipative differential equations. The approach considered is based upon obtaining a sufficient gap in the time dependent linear portion of the equation that corresponds to the linear variational…
In the present paper, a class of partial differential equations related to various plate and rod problems is studied by Lie transformation group methods. A system of equations determining the generators of the admitted point Lie groups…