Bilinear auto-Bäcklund transformations and the hybrid localized wave solutions for the (3+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3+1$$\end{document})-dimensional B-type Kadomtsev–Petviashvili equation

In this paper, we research the hybrid solutions and their interaction of the (3+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3+1$$\end{document})-dimensional B-type Kadomtsev–Petviashvili equation and bilinear auto-Bäcklund transformations of this equation. We first obtain three different kinds of bilinear auto-Bäcklund transformations of this equation by taking advantage of the definition of Hirota bilinear operator; then, we construct the N-soliton solutions via the Hirota bilinear method and extend the N-soliton solutions to the hybrid solutions of some new localized waves by applying the long wave limit method and the complex conjugate condition technique. Meanwhile, the hybrid solutions are summarized, including seven different combinations of L-order kink waves, M-order lump waves and Q-order breather waves. In addition, these hybrid solutions are graphically depicted for us to understand the dynamical behaviors of these solutions.