Solitons of wave equation

Modulated progressive wave solutions (solitons) to (3 + 1) dimensional wave equation are discussed within a general geometrical framework. The role of geodesic coordinates defined by hypersurfaces of Riemannian spaces is pointed out in this context. In particular in E-3 orthogonal geodesic coordinates defined by Dupin cyclides are used to simplify derivation of the most nontrivial results of Friedlander on solitons of (3 + 1)-dimensional wave equations and to correct some of them. The essence of this novel approach is use of the technique of separation of variables in the Kalnins-Miller formulation.