On cyclic symmetries of n-dimensional nonlinear wave equations

Abstract

We consider the three n-dimensional nonlinear wave equations utt = k=1∑n[Fk(u)uxk]xk utt = k=1∑nFk(uxk)uxkxk and utt = k=1∑nFk(uxkxk). We also consider a special class of point transformations. Motivated by the results on the corresponding one-dimensional equations we present a class of discrete symmetries for these equations. In some cases these discrete symmetries form cyclic groups of finite order. Furthermore, point transformations exist that relate different equations but of the same class. The equivalence point transformations for each of the above general equations are presented.