Invariants of two- and three-dimensional hyperbolic equations

Abstract

We consider linear hyperbolic equations of the formWe derive equivalence transformations which are used to obtain differential invariants for the cases n = 2 and n = 3. Motivated by these results, we present the general results for the n-dimensional case. It appears (at least for n = 2) that this class of hyperbolic equations admits differential invariants of order one, but not of order two. We employ the derived invariants to construct interesting mappings between equivalent equations.

A Haar wavelet collocation approach for solving one and two‐dimensional second‐order linear and nonlinear hyperbolic telegraph equations

“…Another numerical approach is given by Jang [12] for nonlinear TE. The author of Reference [13] uses differential invariants. Hosseini et al [14] applied homotopy analysis method.…”

Laplace type invariants for variable coefficient mKdV equations

“…This method was adopted by various scientists and it was then applied to several linear and nonlinear equations with interesting results. [4,[16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. For example, Ibragimov [16] gave a solution to the Laplace problem which consists of finding all invariants of the hyperbolic equations (1).…”

Differential invariants for systems of linear hyperbolic equations

“…In fact, he has proposed a simple method for constructing differential invariants of families of linear and non-linear differential equations admitting infinite equivalence transformation groups [14][15][16]. There is a continuing interest in applying this method on various families of linear and non-linear differential equations [17][18][19][20][21][22][23][24][25][26]. An alternative approach for deriving differential invariants is Cartan's method [27,28].…”