Lie group analysis, Hamiltonian equations and conservation laws of Born-Infeld equation (Q2925277)

The Lie symmetry group method and, in particular, the invariance under point transformations are used to obtain solutions to the Born-Infeld equations. The motivation is that the Born-Infeld theory and its nonabelian extensions have met a revival of interest, among other things due to the connections with string theory. In this paper, the Lie point symmetries of the Born-Infeld equations are first established and then they are used to obtain the classical similarity solutions. A short overview of methods to find the Lie algebras of a differential equation system is presented and then they are applied to the determination of the reduced equations including similarity solutions. Finally, the Hamilton equations including the Hamiltonian symmetry group and the conservation laws are determined. The connections with other methods like those based on the rational function transformations or on software such as Maple and Mathematica are presented.