Abstract
This paper studies the solitons of Radhakrishnan-Kundu-Lakshma- nan (RKL) model with power law nonlinearity. The modified simple equation method and $ \exp(-\varphi({q}) $) method are presented as integration mechanisms. Dark, bright, singular and periodic soliton solutions are extracted as well as the constraint conditions for their existence. A prized discussion on the stability of these soliton profiles on the basis of index of the power law nonlinearity is also carried out with the help of physical description of solutions. The integration techniques have been proved to be extremely efficient and robust to find new optical solitary wave solutions for various nonlinear evolution equations describing optical pulse propagation. Moreover, using linear stability analysis, modulation instability of the RKL model is studied. Different effects contributing to the modulation instability spectrum gain are analyzed.
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