Abstract
This paper investigates the most straightforward extension of the (2+1) dimensional Nonlinear Schrödinger (NLS) equation, termed the Fokas system. The evolution equation is trilinearized, employing a unique method called Truncated Painlevé Approach (TPA) for the (2+1) dimensional Fokas System (FS). 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.
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