A symmetry classification for a class of (2+1)-nonlinear wave equation

Abstract

In this paper, a symmetry classification of a (2 + 1)-nonlinear wave equation u tt − f (u)(u xx + u yy ) = 0 where f (u) is a smooth function on u, using Lie group method, is given. The basic infinitesimal method for calculating symmetry groups is presented, and used to determine the general symmetry group of this (2 + 1)-nonlinear wave equation.

Preliminarily group classification of a class of 2D nonlinear heat equations

“…(1.1) via the so-called method of preliminary group classification. This method was suggested in [10] and applied when an equivalence group is generated by a finite-dimensional Lie algebra g E . The essential part of the method is the classification of all nonsimilar subalgebras of g E .…”

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.…”

Symmetry Analysis of Telegraph Equation

“…This problem is attacked by the naive approach of taking a general element in the Lie algebra and subjecting it to various adjoint transformations so as to simplify it as much as possible. The idea of using the adjoint representation for classifying group-invariant solutions is due to [2,4,7,8].…”