Multiple soliton solutions and rational solutions for the (2+1)-dimensional dispersive long water–wave system

In this work we study the (2+1)-dimensional dispersive long water–wave system. We employ the Painlevé–Bäcklund transformation and the simplified Hirota's method to derive multiple soliton solutions. We also determine a variety of traveling wave solutions and rational solutions of distinct physical structures.

► We study the dispersive long water–wave system.
► We derive multiple soliton solutions by using the Painlevé–Bäcklund transformation.
► We also establish a variety of other traveling wave solutions.