Notes on solitary-wave solutions of Rosenau-type equations

The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of three different forms are derived. The results depend on some conditions on the speed of the waves with respect to the parameters of the equations. They are discussed for several families of Rosenau equations present in the literature. The analysis is illustrated with a numerical study of generation of approximate solitary-wave profiles from a numerical procedure based on the Petviashvili iteration.