Bilinear auto-Ba¨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\ddot{\mathrm{a}}}}$$\end{document}cklund transformations and higher-order breather solutions for the (3+1)-dimensional generalized KdV-type equation

The (3+1)-dimensional generalized KdV-type equation has been found to model many physical, mechanical and engineering phenomena, including geophysical fluid dynamics, ocean engineering and plasma physics. Using the Hirota bilinear method, four bilinear auto-Ba¨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\ddot{\mathrm{a}}}}$$\end{document}cklund transformations of this equation are derived explicitly. The hyperbolic cosine function solution and exponential function solutions are obtained by assuming different forms of solutions. Based on the N-soliton solutions, different localized wave structures interaction behaviors and relevant dynamics features are discussed and analyzed graphically by using the complex conjugate condition technique. Some conditions for the existence of hybrid solutions are summarized, including the M-order kink soliton solution, L-order breathers solution, the hybrid solution between M-order kink solitons and L-order breathers. Novel hybrid solutions for the (3+1)-dimensional generalized KdV-type equation obtained in this work can be of great importance in nonlinear sciences.