Solitons for the (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid via the Pfaffian technique

Abstract

Fluids are common in nature, the study of which helps the design of the related industries. Under investigation in this letter is the (2[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation for an irrotational incompressible fluid. Pfaffian solutions have been obtained based on the Pfaffian technique with the assistance of the real auxiliary function [Formula: see text]. N-soliton solutions with [Formula: see text] are constructed, where y is the scaled space coordinate and [Formula: see text] is the steady stream function in the irrotational incompressible flow. Background shapes of the solutions are affected by [Formula: see text], but the structures of the solutions are affected by the derivative of the log terms in the solutions. Neighborhoods at the origins of the solitons are different in consequence of the different values of the real auxiliary parameter a. One- and two-soliton solutions are illustrated, which are the superpositions of the two kink solitons and different forms of [Formula: see text]. Interactions of the two solitons are presented, from which we see that the velocities, amplitudes and shapes of the two solitons remain unchanged before and after each interaction.