Optical soliton solutions of the Biswas-Arshed model by the $\tan(\circleddash/2)$ expansion approach

TL;DR

This paper derives exact optical soliton solutions of the Biswas-Arshed model using the $ an( riangle/2)$ expansion method, revealing various wave phenomena like shock waves, rogue waves, and interactions relevant for optical fiber applications.

Contribution

It introduces a novel application of the $ an( riangle/2)$ expansion scheme to the Biswas-Arshed model, producing new exact soliton solutions with detailed physical interpretations.

Findings

Discovery of optical shock waves and rogue waves in the model

Amplitude behavior of solitons during interactions and over time

Graphical analysis illustrating physical wave phenomena

Abstract

In this paper, we consider the Biswas-Arshed model (BAM) with nonlinear Kerr and power law. We integrate these nonlinear structures of the BAM to obtain optical exact solitons that passing through the optical fibers. To retrieve the solutions, we apply the $\tan(\circleddash/2)$ expansion integral scheme to the structures of the BAM nonlinearity. The novel solutions present optical shock wave, double periodic optical solitons, interaction between optical periodic wave and optical solitons, and optical periodic and rogue waves for both structures of the model. It is shown that the amplitude of the periodic double solitons waves gradually increases and reached the highest peak at the moment of interaction, and it goes to diminish for a much larger time. In fact, we show that the amplitude of the wave for the interaction between periodic and optical solitons, gradually increases with beat phenomena. To the purpose, all these types of optical solitons can be frequently used to amplify or reduce waves for a certain hight. Moreover, we describe the physical phenomena of the solitons in graphically.