Non-collisional Behaviour of Novel Nonlinear Wave Patterns for (2+1) Dimensional Fokas System

Abstract

This paper investigates the most straightforward extension of the (2+1) dimensional NLS equation, termed the Fokas system. The evolution equation is trilinearized, employing a unique method called Truncated Painlev\'{e} Approach for the (2+1) dimensional Fokas system. In terms of arbitrary functions, this method finds relatively extensive classes of solutions. Localized solutions, including dromion triplet, lump, multi-compacton and multi-rogue wave are generated by efficiently utilizing arbitrary functions. The analysis reveals that the localized solutions evolved do not move in space and only their amplitude changes with time.