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

Considering the importance of higher dimensional equations widely applied to real nonlinear problems, many (4+1)-dimensional integrable systems have been established through 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 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 by means of the mulitilinear variable separation approach for the 4DBLMP equation. In addition, making advantages 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.