Bilinear auto-Bäcklund transformation, breather-wave and periodic-wave solutions for a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

Incompressible fluids are seen in ocean engineering, biomechanics, astrophysics, etc. A (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation is hereby investigated. With the help of the Hirota method and symbolic computation, we present a bilinear auto-Bäcklund transformation with some analytic solutions. Based on the existing N -soliton solutions, we determine the higher-order breather solutions, where N is a positive integer. Via the Hirota-Riemann method, we derive the periodic-wave solutions. Graphical representations of the second-order breather and periodic waves are investigated. Moreover, we graphically present the second-order breather and periodic waves with the influence of the coefficients in that equation. Our results might be helpful to understand certain nonlinear phenomena in fluid mechanics.