Peaked Traveling Wave Solutions to a Generalized Novikov Equation with Cubic and Quadratic Nonlinearities

Abstract

The Camassa-Holm equation, Degasperis—Procesi equation and Novikov equation are the three typical integrable evolution equations admitting peaked solitons. In this paper, a generalized Novikov equation with cubic and quadratic nonlinearities is studied, which is regarded as a generalization of these three well-known studied equations. It is shown that this equation admits single peaked traveling wave solutions, periodic peaked traveling wave solutions, and multi-peaked traveling wave solutions.