New Symmetries in Mathematical Physics Equations
G. A. Kotel'nikov
Abstract
An algorithm for studing the symmetrical properties of the partial differential equation of the type Lu=0 is proposed. By symmetry of this equation we mean the operators Q satisfying commutational relations of order p more than p=1 on the solutions u: [L...[L,Q]...]u=0. It is shown, that within the framework of the proposed method with p=2 the relativistic D'Alembert and Maxwell equations are the Galilei symmetrical ones. Analogously, with p=2 the Galilei symmetrical Schroedinger equation is the relativistic symmetrical one. In both cases the standard symmetries are realized with p=1.
Create a lesson
Related papers
High-order compact ALE gas-kinetic scheme on three-dimensional unstructured meshes
Yibo Wang, Xing Ji, Liang Pan
Multiplicity and parity in Hirota's N-soliton conditions: the bilinear families L\,(Dx3+Λ)2n+1
Shi Zhenhua
An exact unstable mode of self-similar Yang--Mills solutionsin 5+1 dimensions
Piotr Bizoń
Lorentz-Invariant Measure for Path Integrals in the Future Cone
Vladimir V. Belokurov, Vsevolod V. Chistiakov, Klavdiia A. Lursmanashvili et al.
An Excursion into Grassmannian Spectra
Dmitri Bykov, Viacheslav Krivorol
Eigenstates on O-algebras with an application to ladder operators
Fabio Bagarello, Hiroshi Inoue, Salvatore Triolo