High-dimensional nonlinear variable separation solutions and novel wave excitations for the (4 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Abstract

Abstract Considering the importance of higher-dimensional equations that are widely applied to real nonlinear problems, many (4 + 1)-dimensional integrable systems have been established by uplifting the dimensions of their corresponding lower-dimensional integrable equations. Recently, an integrable (4 + 1)-dimensional extension of the Boiti–Leon–Manna–Pempinelli (4DBLMP) equation has been proposed, which can also be considered as an extension of the famous Korteweg–de Vries equation that is applicable in fluids, plasma physics and so on. It is shown that new higher-dimensional variable separation solutions with several arbitrary lower-dimensional functions can also be obtained using the multilinear variable separation approach for the 4DBLMP equation. In addition, by taking advantage of the explicit expressions of the new solutions, versatile (4 + 1)-dimensional nonlinear wave excitations can be designed. As an illustration, periodic breathing lumps, multi-dromion-ring-type instantons, and hybrid waves on a doubly periodic wave background are discovered to reveal abundant nonlinear structures and dynamics in higher dimensions.