Parametric representations of multisoliton solutions of the generalized short pulse equations (Mathematical aspects of nonlinear waves and their applications)

Abstract

We consider three novel PDEs associated with the integrable generalizations of the short pulse equation classified recently by Hone et al (2018 Lett. Math. Phys. 108 927-947). In particular, we obtain a variety of exact solutions by means of a direct method combined with the reciprocal transformations. We report the main results associated with soliton solutions. Specifically, we present the parametric representations of multisoliton solutions. These solutions include cusp solitons, unbounded solutions with finite slope and breathers. In addition, the cusped periodic wave solutions are constructed from the cusp solitons by means of a simple procedure. The new features of solutions are exemplified for both the cusp solitons and cusped periodic waves.