Tanh-peakon and hyperbolicon of a nonlinear-strength shallow water wave equation

This paper introduces a new shallow water wave equation with nonlinear strength. By using peakon bifurcation equation, we show that as the nonlinear-strength parameter varies, this nonlinear-strength equation has many interesting new solutions, which are called tanh-peakon and hyperbolicon because they can be expressed as tanh and hyperbolic functions. Exact expression of these new solution are detailed derived.