Elusive exotic structures and their collisional dynamics in (2+1)-dimensional Boiti-Leon-Pempinelli equation

Abstract

Abstract In this paper, we investigate the (2+1) dimensional Boiti-Leon-Pempinelli (BLP) equation employing truncated Painlevé expansion approach and extract a plethora of localized nonlinear waves, including multi-dromions, multi-lumps, multi-rogue waves, generalized-breathers etc. The dromions are characterized as bright, dark and mixed (bright-dark) based on their intensity. The collisional dynamics of dromions shows that they change their shape or form upon interaction in addition to undergoing a phase change. The lump solutions of orders one and two are also extracted through appropriate test functions and observed to be non-interacting in nature. Also, the first-order and second-order rogue waves are also obtained through rational polynomials and shown to be unstable. The generalized breathers are obtained by utilizing the three-wave test function. The highlights of our investigation is that one encounters a strange coherent structure called ‘dromion filter’ which contains a dynamic and a stationary dromion. In addition, we are also able to unearth a ‘coexistent dromion-line soliton’.