Study of the generalization of regularized long-wave equation

A generalization of the regularized long-wave equation is considered, and the existences of smooth soliton, peakon, and periodic solutions are established via the complete discrimination system for polynomial method and the bifurcation method. Concrete examples of these solutions are constructed to verify our conclusions directly. In particular, we construct a special kind of smooth soliton solution, namely a Gaussian soliton solution, and give two sufficient conditions for the existence of such a solution by the extended trial equation method. To the best of our knowledge, this is the first time that a Gaussian soliton solution has been constructed for an equation with no logarithmic nonlinearity.