Symmetry Analysis of Telegraph Equation

Abstract

Lie symmetry group method is applied to study the Telegraph equation. The symmetry group and its optimal system are given, and group invariant solutions associated to the symmetries are obtained. Finally the structure of the Lie algebra symmetries is determined.

Lie group analysis, Hamiltonian equations and conservation laws of Born–Infeld equation

“…The results are in Table 2. Thus the set of new linear independent multipliers are 5 (x 2 − u 2 )tut − 1 2 u 3 + x 2 u 1 2 (u 2 − x 2 )t 2 ux v 6 (u 2 + t 2 )xut + xt 1 2 (t 3 + u 2 )xux + t 2 u + 1 2 u 3 v 7 2xtuut + 3 2 xu 2 + xuut …”

“…In physics, the Born-Infeld theory is a nonlinear generalization of electromagnetism [6,5]. The model is named after physicists Born and Infeld (1898-1968) who first proposed it.…”