Related papers: The Canonical Symmetry for Integrable Systems
Inspired by ideas from non-commutative geometry, unions of moduli spaces of linear control systems are identified as open subsets of infinite Grassmannians.
Conservation laws vanishing along characteristic directions of a given system of PDEs are known as characteristic conservation laws, or characteristic integrals. In 2D, they play an important role in the theory of Darboux-integrable…
We remark on the existence of non-linearly realized conformal symmetries for scalar adiabatic perturbations in cosmology. These conformal symmetries are present for any cosmological background, beyond any slow-roll or quasi-de Sitter…
Lie symmetries of a Novikov geometrically integrable equation are found and group-invariant solutions are obtained. Local conservation laws up to second order are established as well as their corresponding conserved quantities. Sufficient…
For difference variational problems on lattice, this paper presents a relation between divergence variational symmetries and conservation laws for the associated Euler-Lagrange system provided by Noether's theorem. This hence inspires us to…
In this paper we consider the relation between symmetries and first integrals for both continuous canonical Hamiltonian equations and discrete Hamiltonian equations. We observe that canonical Hamiltonian equations can be obtained by…
Nonlinear self-adjointness method for constructing conservation laws of partial differential equations (PDEs) is further studied. We show that any adjoint symmetry of PDEs is a differential substitution of nonlinear self-adjointness and…
We consider compositions of the transformations of the time variable and canonical transformations of the other coordinates, which map completely integrable system into other completely integrable system. Change of the time gives rise to…
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the…
The conservation laws of the third order quasilinear scalar evolution equations are considered via differential system and characteristic cohomology. We find a subspace of 2 forms in the infinite prolonged space in which every conservation…
Two-component second and third-order Burgers type systems with nondiagonal constant matrix of leading order terms are classified for higher symmetries. New symmetry integrable systems with their master symmetries are obtained. Some third…
In this paper, we construct and analyse the symmetries and conservation laws (conserved densities) of a model of a nonlinear Scrodinger equation with PT-symmetric potentials and inhomogeneity.
We examine the reductions of the order of certain third- and second-order nonlinear equations with arbitrary nonlinearity through their symmetries and some appropriate transformations. We use the folding transformation which enables one to…
Nonlocal symmetries for exactly integrable two-field evolutionary systems of the third order have been computed. Differentiation of the nonlocal symmetries with respect to spatial variable gives a few nonevolutionary systems for each…
The symmetry structure of twodimensional nonlinear isotropic oscillator, introduced in Physica D237 (2008) 505, is discussed. It is shown that it possesses three independent integrals of motion which can be chosen in such a way that they…
Microscopic symmetries impose strong constraints on the elasticity of a crystalline solid. In addition to the usual spatial symmetries captured by the tensorial character of the elastic tensor, hidden non-spatial symmetries can occur…
The Liouville equation is well known to be linearizable by a point transformation. It has an infinite dimensional Lie point symmetry algebra isomorphic to a direct sum of two Virasoro algebras. We show that it is not possible to discretize…
Transitive consistency is an intrinsic property for collections of linear invertible transformations between Euclidean coordinate frames. In practice, when the transformations are estimated from data, this property is lacking. This work…
Lie group analysis of differential equations is a generally recognized method, which provides invariant solutions, integrability, conservation laws etc. In this paper we present three characteristic examples of the construction of invariant…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…