Method of Replacing the Variables for Generalized Symmetry of D'Alembert Equation
Kotel'nikov, G. A.
arXiv, 0012018 / Harvested from arXiv
By symmetry of the partial differential equation L'\phi'(x')=0 with respect to the variables replacement x'=x'(x), \phi'=\phi'(\Phi\phi) it is advanced to understand the compatibility of engaging equations system A\phi'(\Phi\phi)=0, L\phi(x)=0, where A\phi'(\Phi\phi)=0 is obtained from the initial equation by replacing the variables, L'=L, \Phi(x) is some weight function. If the equation A\phi'(\Phi\phi)=0 may be transformed to the form L(\Psi\phi)=0, where \Psi(x) is the weight function, the symmetry will be named the standard Lie symmetry, otherwise the generalized symmetry. It is shown that with the given understanding of the symmetry, D'Alembert equation for one component field is invariant with respect to any arbitrary reversible coordinate transformations x'=x'(x). In particular, they contain the transformations of the conformal and Galilei groups realizing the type of standard and generalized symmetry for \Phi(x)=\phi'(x'\to x)/\phi(x).
Publié le : 2000-12-08
Classification:  Physics - Classical Physics,  Mathematical Physics
@article{0012018,
     author = {Kotel'nikov, G. A.},
     title = {Method of Replacing the Variables for Generalized Symmetry of D'Alembert
  Equation},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0012018}
}
Kotel'nikov, G. A. Method of Replacing the Variables for Generalized Symmetry of D'Alembert
  Equation. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0012018/