Abstract
 In the present work, the First Integral Method is being applied in finding a non-soliton as well as a soliton solution of the ( 2 + 1 ) dimensional Kundu-Mukherjee-Naskar (KMN) equation which is a variant of the well-known Nonlinear Schrodinger ( NLS ) equation. Using the method, a dark optical soliton solution and a periodic trigonometric solution to the KMN equation have been suggested and the relevant conditions which guarantee the existence of such solutions are also indicated therein. Â
Highlights
Optical solitons are pulses which compose the basic fabric of signal transmission across trans-continental and trans-oceanic distances in telecommunication engineering
We describe an algorithm of the First Integral Method and it is applied in solving the KMN equation
Feng and was further developed by himself. This method had been effectively applied by many authors in solving different types of Nonlinear Evolution Equations (NLEEs) encountered in the study of science and engineering
Summary
Optical solitons are pulses which compose the basic fabric of signal transmission across trans-continental and trans-oceanic distances in telecommunication engineering. This equation was first proposed in the year 2014 by three Indian physicists namely Anjan Kundu, Abhik Mukherjee and Tapan Naskar for modelling the dynamics of two-dimensional rogue waves in ocean water and two-dimensional ion-acoustic waves in magnetized plasmas [7,8] We can consider this equation as an extension of the well-known Nonlinear Schrodinger (NLS) equation. The equation was proposed by Kundu, Mukherjee and Naskar to describe oceanic rogue waves as well as hole waves, it may be used in describing optical waves or soliton propagation through Erbium doped coherently excited resonant wave-guides This equation can be used in the study of the phenomenon of bending of light beams. We describe an algorithm of the First Integral Method and it is applied in solving the KMN equation
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