Novel optical solitons patterns via Biswas–Arshed equation with gain or loss. Modulated wave gain

The Biswas–Arshed equation (BAE) with space–time dispersion was currently considered in the literature. Optical phenomena embedded in this equation are self-steepening, self-phase modulation and Raman scattering. Here, we consider BAE with gain or loss. It is worth mentioning that the gain or loss has an impact on blowup or decaying solitons propagation in optical fibers, which is novel. Our objective is to find optical soliton solutions of BAE and the aforementioned physical phenomena are investigated in some details. The conditions for the dominance of a phenomenon are predicted. This is physically important to inspect the behavior of solitons prpagation. To this issue, exact solutions of the model equation are derived by using the unified method. The solutions obtained are displayed graphically. Dark soliton, bright soliton, M-shaped soliton, rhombus soliton (which is novel) and chirped soliton with tunneling are observed. The modulation instability is studied and it is found that it triggers when the coefficients of the space–time dispersions are positive.