Multi-soliton solutions of the BBM equation arisen in shallow water

Abstract

In this work, multiple soliton solutions and multiple singular soliton solutions are formally derived for the BBM equation. A novel transformation method combined with the Hirota's bilinear method are used to determine the two sets of solutions, where each set has a distinct structure. The resonance phenomenon does not exist for the model under the study. 2016 All rights reserved.