Related papers: Integrability in differential coverings
We provide a given algebraic structure with the structure of an infinitesimal algebraic skeleton. The necessary conditions for integrability of the absolute parallelism of a tower with such a skeleton are dispersive nonlinear models and…
We establish a version of the first Noether Theorem, according to which the (equivalence classes of) conserved quantities of given Euler-Lagrange equations in several independent variables are in one-to-one correspondence with the…
An extension of the supersymmetric U model for correlated elctrons is given and integrability is established by demonstrating that the model can be constructed through the Quantum Inverse Scattering Method using an R-matrix without the…
The negative integrable hierarchies of shallow water waves and dispersionless Toda lattice equations are considered. The integrability is shown by explicit construction of an infinite set of conservation laws.
We carry out an extensive investigation of conservation laws and potential symmetries for the class of linear (1+1)-dimensional second-order parabolic equations. The group classification of this class is revised by employing admissible…
For partial differential equations (PDEs) that have $n\geq2$ independent variables and a symmetry algebra of dimension at least $n-1$, an explicit algorithmic method is presented for finding all symmetry-invariant conservation laws that…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
Conservation laws of a class of time-dependent damped nonlinear multidimensional wave equations are derived by Noether's theorem. For arbitrary nonzero damping coefficient and nonlinear interaction term, its infinitesimal variational…
This paper is purposed to exploit prevalent premises for determining analytical solutions to differential equations formulated from the calculus of variations. we realize this premises from the statement of Emmy Noether's theorem; that…
Preservation of linear and quadratic invariants by numerical integrators has been well studied. However, many systems have linear or quadratic observables that are not invariant, but which satisfy evolution equations expressing important…
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent…
We present an infinite series of autonomous discrete equations on the square lattice possessing hierarchies of autonomous generalized symmetries and conservation laws in both directions. Their orders in both directions are equal to $\kappa…
In this paper we consider a class of semihamiltonian systems characterized by the existence of a special conservation law. The density and the current of this conservation law satisfy a second order system of PDEs which has a natural…
This paper mainly contributes to the extension of Noether's theorem to differential-difference equations. For that purpose, we first investigate the prolongation formula for continuous symmetries, which makes a characteristic representation…
The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general…
We discuss the interrelations between symmetry of an Ito stochastic differential equations (or systems thereof) and its integrability, extending in party results by R. Kozlov [J. Phys. A ${\bf 43}$ (2010) \& ${\bf 44}$ (2011)]. Together…
In this note a new way to construct the characteristics of conservations laws of integrable chiral-type systems is proposed.
The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the…
We describe differential invariants of infinite-dimensional algebras being equivalence algebras of some classes of PDE and study structure of these algebras.
We present a brief overview of integrability of nonlinear ordinary and partial differential equations with a focus on the Painleve property: an ODE of second order has the Painleve property if the only movable singularities connected to…