Analysing of different wave structures to the dissipative NLS equation and modulation instability

This study investigates the (1+1) dimensional dissipative nonlinear Schrödinger equation, which has applications in modeling the evolution of swell in the ocean. Two different and impressive techniques are used for the solutions, which are the Jacobi elliptic function expansion method and the sine-Gorgon expansion method. The suggested techniques are designed to derive the solutions for many other the nonlinear partial differential equations that arising in various branches of sciences. By applying this methods, we obtain novel soliton solutions, which are expressed in terms dark, bright, singular and combo optical solitons. The efficient optical soliton solutions discovered through this methods have the potential to find use in a variety of fields, inclusive electronics, ocean waves, and optical fibers. The modulation instability criterion for governing model is obtained based on the standard linear stability analysis. Additionally, we will also present graphs in 2D and 3D form with constraints conditions.