Some aspects of the group invariant solutions of wave propagation for an electric field


This paper deals with the investigation of the solution of wave propagation of an electric field in a source free, linear, isotropic, homogeneous region described by the Helmholtz equation

Ñ2 u + k2 u = 0

where u is wave function, k is wave number, Ñ is Laplacian-operator. The solution obtained from the general prolongation formula for the closed form of the symmetry group. The results presented here are general in nature and include the results previously examined by several authors. The benefit of using the general prolongation method is that the invariant solution of the Helmholtz equation involves linearity, rotation and scaling symmetries.

2020 Mathematical Sciences Classification: 17B66, 22E70, 46N50, 70G65, 81R05.  

Keywords: – Space invariance, Linearity, Translation, Scaling, Rotation.

Kapil Pal1*, V. G. Gupta2, Hoshiyar Singh3, Vatsala Pawar4