Abstract
In this work, the Kundu-Mukherjee-Naskar (KMN) equation that addresses the optical soliton dynamics in (2 +1)-dimensions is studied via two novel techniques, which are the Cole-Hopf transform based method and Wang’s direct mapping method for the first time. Firstly, based on the Cole-Hopf transform, the symbolic computation with the ansatz function schemes are employed to construct the abundant soliton solutions. Some new soliton solutions including the rational breathe, cross-periodic, multi-wave, double exponential form and interaction soliton solutions are obtained. Secondly, Wang’s direct mapping method is adopted to seek for the breather, bright-dark and kinky periodic soliton solutions. Meanwhile, the behaviors of the different soliton solutions are presented in the form of 3-D plot, 2-D contour and 2-D curve. The ideas in this work are expected to provide some new enlightenment for the study of the exact soliton solutions of the PDEs in the optics.
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