Novel localized waves and dynamics analysis for a generalized (3+1)-dimensional breaking soliton equation

Purpose This paper aims to explore new variable separation solutions for a new generalized (3 + 1)-dimensional breaking soliton equation, construct novel nonlinear excitations and discuss their dynamical behaviors that may exist in many realms such as fluid dynamics, optics and telecommunication. Design/methodology/approach By means of the multilinear variable separation approach, variable separation solutions for the new generalized (3 + 1)-dimensional breaking soliton equation are derived with arbitrary low dimensional functions with respect to {y, z, t}. The asymptotic analysis is presented to represent generally the evolutions of rogue waves. Findings Fixing several types of explicit expressions of the arbitrary function in the potential field U, various novel nonlinear wave excitations are fabricated, such as hybrid waves of kinks and line solitons with different structures and other interesting characteristics, as well as interacting waves between rogue waves, kinks, line solitons with translation and rotation. Research limitations/implications The paper presents that a variable separation solution with an arbitrary function of three independent variables has great potential to describe localized waves. Practical implications The roles of parameters in the chosen functions are ascertained in this study, according to which, one can understand the amplitude, shape, background and other characteristics of the localized waves. Social implications The work provides novel localized waves that might be used to explain some nonlinear phenomena in fluids, plasma, optics and so on. Originality/value The study proposes a new generalized (3 + 1)-dimensional breaking soliton equation and derives its nonlinear variable separation solutions. It is demonstrated that a variable separation solution with an arbitrary function of three independent variables provides a treasure-house of nonlinear waves.