Related papers: The Gardner method for symmetries
We consider the issue of correspondence between symmetries and conserved quantities in the class of linear relativistic higher-derivative theories of derived type. In this class of models the wave operator is a polynomial in another…
A new integrable discrete system is constructed and studied, based on the algebraization of the difference operator. The model is named the discrete generalized nonlinear Schrodinger (GNLS) equation for which can be reduced to classical…
A generalization of implicit conservative numerics to multiple dimensions requires advanced concepts of tensor analysis and differential geometry and hence a more thorough dedication to mathematical fundamentals than maybe expected at first…
In this paper, We derive the symmetry group theorem to the Lin-Tsien equation by using the modified CK's direct method, from which we obtain the corresponding symmetry group. More importantly, conservation laws corresponding to the…
The Newton-Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is…
The Gauss-Seidel method has been used for more than 100 years as the standard method for the solution of linear systems of equations under certain restrictions. This method, as well as Cramer and Jacobi, is widely used in education and…
We embark on a systematic study of continuous non-invertible symmetries, focusing on 1+1d CFTs. We describe a generalized version of Noether's theorem, where continuous non-invertible symmetries are associated to $\textit{non-local}$…
In this paper we study symmetries, Newtonoid vector fields, conservation laws, Noether's Theorem and its converse, in the framework of the $k$-symplectic formalism, using the Fr\"olicher-Nijenhuis formalism on the space of $k^1$-velocities…
We discuss the relation between symmetries and conservation laws in the realm of classical field theories based on the Hamiltonian constraint. In this approach, spacetime positions and field values are treated on equal footing, and a…
The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the $A_{3}$-generalization where fields take value in $SU(2)$ describes integrable deformations of conformal field…
Symmetry postulates play a crucial role in various approaches to reconstruct quantum theory from a few basic principles. Discrete and continuous symmetries are under consideration. The continuous case better matches the physical needs for…
Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are…
An energy conservative discontinuous Galerkin scheme for a generalised third order KdV type equation is designed. Based on the conservation principle, we propose techniques that allow for the derivation of optimal a priori bounds for the…
We consider symmetries and perturbed symmetries of canonical Hamiltonian equations of motion. Specifically we consider the case in which the Hamiltonian equations exhibit a Lambda symmetry under some Lie point vector field. After a brief…
We explicitly construct the series expansion for a certain class of solutions to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric solutions. We express the Taylor coefficients through some universal combinatorial…
Utilizing some conservation laws of (1+1)-dimensional integrable local evolution systems, it is conjectured that higher dimensional integrable equations may be regularly constructed by a deformation algorithm. The algorithm can be applied…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
A geometric framework, called multicontact geometry, has recently been developed to study action-dependent field theories. In this work, we use this framework to analyze symmetries in action-dependent Lagrangian and Hamiltonian field…