Related papers: The Gardner method for symmetries
A systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation. Such solutions are analytic in the spatial variable $x$ and the temporal variable $t,$ and they are…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
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…
This paper presents two kinds of strategies to construct structure-preserving algorithms with homogeneous Neumann boundary conditions for the sine-Gordon equation, while most existing structure-preserving algorithms are only valid for zero…
A generalization of classical cubic B-spline functions with a parameter is used as basis in the collocation method. Some initial boundary value problems constructed on the nonlinear Klein-gordon equation are solved by the proposed method…
The method of nonlinear self-adjointness is applied to the Kadomtsev-Petviashvili equation. The infinite set of conservation laws associated with the infinite algebra of Lie point symmetry of the KP equation is constructed.
The direct method based on the definition of conserved currents of a system of differential equations is applied to compute the space of conservation laws of the (1+1)-dimensional wave equation in the light-cone coordinates. Then Noether's…
Symmetries are defined in histories-based theories paying special attention to the class of history theories admitting quasitemporal structure (a generalization of the concept of `temporal sequences' of `events' using partial semigroups)…
There exist instances of dynamical systems possessing symmetry transformations of which the conserved Noether charges generating these symmetries feature an explicit time dependence in their functional representation over phase space. The…
We discuss general properties of the conservation law associated with a local symmetry. Using Noether's theorem and a generalized Belinfante symmetrization procedure in 3+1 dimensions, a symmetric energy-momentum (pseudo) tensor for the…
In this paper, by applying the multiplier method we obtain a complete classification of low-order local conservation laws for a generalized seventh-order KdV equation depending on seven arbitrary nonzero parameters. We apply the Lie method…
A general theorem on conservation laws for arbitrary difference equations is proved. The theorem is based on an introduction of an adjoint system related with a given difference system, and it does not require the existence of a difference…
The deformed supersymmetric sine-Gordon model, obtained through known deformation of the corresponding potential, is found to be quasi-integrable, like its non-supersymmetric counterpart, which was observed earlier. The system expectedly…
We present a novel approach in constructing deviations of the Kerr spacetime whereas the symmetries can be preserved. The method was applied trivially in all known classical black-hole spacetimes tested, while provides the possibility of…
We study a subclass of Horndeski gravity which has both global conformal and shift symmetries. Global symmetries are characterised by the presence of a conserved current which has been shown to be of particular importance for the…
We examine the question of the integrability of the recently defined $\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate…
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 apply a novel method for the equivalence group and its infinitesimal generators to the investigation of invariants of linear ordinary differential equations. First, a comparative study of this method is illustrated by an example. Next,…
We study general metric-affine theories of gravity in which the metric and connection are the two independent fundamental variables. In this framework, we use Lagrange-Noether methods to derive the identities and the conservation laws that…
Infinitely many nonlocal symmetries and conservation laws of the (1+1)-dimensional Sine-Gordon (SG) equation are derived in terms of its B\"acklund transformation (BT). Some special nonlocal symmetries and nonlocal conservation laws are…