Abstract
Recently, Anjan Kundu, Abhik Mukherjee and Tapan Naskar (KMN) have introduced a (2+1)-dimensional equation as a new extension of the well-known nonlinear Schrödinger (NLS) equation, which is called KMN equation in this paper. We provide a triplet Lax pair of the KMN equation. Basing on triplet Lax pair, we present the first-order rogue wave (RW) solution of the KMN equation by the one-fold Darboux transformation from a non-zero “seed” solution. This RW solution also satisfies the complex modified Korteweg–de Vries (mKdV) and the NLS equation by two different transformations of variables. Moreover, we discuss the localization of rogue wave of KMN equation, observing that the area of rogue wave is a constant which is just related to the amplitude of seed solution.
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