On a (3+1)-dimensional Boiti–Leon–Manna–Pempinelli Equation

Abstract

The Boiti-Leon-Manna-Pempinelli (BLMP) equation is seen as a model for the incompressible fluid. In this article, a (3+1)-dimensional BLMP equation is investigated. With the aid of the Bell polynomials, bilinear form of such an equation is obtained. By virtue of the bilinear form, two kinds of soliton solutions with different nonlinear dispersion relations and another kind of analytic solutions are derived. Lax pairs and Bäcklund transformations are also constructed. Soliton propagation and interaction are analysed: (i) solitions with different nonlinear dispersion relations have different velocities and backgrounds; (ii) for another kind of analytic solutions with different nonlinear dispersion relations, the periodic property is displayed.

Pfaffian and extended Pfaffian solutions for a (3+1)-dimensional generalized wave equation

“…Note that the bilinear form for equation (1) has been obtained in [12,19] via the dependent variable transformation u=−2(ln f ) x . In this paper, we will take a generalised dependent variable transformation in the [20]…”

On some new soliton solutions of (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation using two different methods

“…which was derived by Boiti et al when they researched a Korteweg-de Vries (KdV) equation through weak Lax pairs relations (Boiti, Leon, Manna, & Pempinelli, 1986). Many researchers discussed the BLMP equation (Darvishi, Najafi, Kavitha, & Venkatesh, 2012;Li & Ma, 2018;Liu, Du, Zeng, & Nie, 2017;Liu, Tian, & Hu, 2018;Mabrouk & Rashed, 2017;Osman & Wazwaz, 2019;Peng, Tian, & Zhang, 2019;Tang & Zai, 2015;Wu, Liu, Piao, Zhuang, & Wang, 2020;Xu, 2019;Zuo, Gao, Yu, Sun, & Xue, 2015). The modified form of Eq.…”

Breather wave and lump‐type solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation in incompressible fluid

“…Darvishi et al 2 presented the stair and step soliton solutions. Zuo et al 3 derived the bilinear form, Lax pairs, and Bäcklund transformations. Tang and Zai 4 obtained the new periodic‐wave solutions.…”