Lump solution and interaction solutions to the fourth-order extended (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

Abstract In this paper, we explore the exact solutions to the fourth-order extended (2+1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Based on Hirota bilinear method, lump solution, periodic cross-kink solutions and bright-dark soliton solutions were investigated. By calculating and solving, the peak and trough of lump solution are obtained, and the maximum and minimum points of each are solved. The three-dimensional plots and density plots of periodic cross-kink solution and bright-dark soliton solution are drawn and the dynamics of solutions under different parameters are observed.