Brownian motion effects on W-shaped soliton and modulation instability gain of the (2+1)-dimensional nonlinear schrödinger equation.

Investigation of soliton solutions and Modulation Instability (MI) analysis to the (2+1)-Stochastic Chiral Nonlinear Schrödinger Equation (SCNLSE) having noise force and Brownian movement (BM) have been done in this work. We first use the transformation technic and auxiliary equation method (AEM) to establish three types of soliton solutions. Depending on the constraint relation set on the auxiliary equation parameters, it is obtained bright and dark soliton solutions. Thereafter, taking the same different parameters it is gained the combined bright-dark soliton, bright-bright soliton solutions. By employing suitable values of the used parameters together with the model parameters it is show out W-shaped soliton solutions. Throughout the paper it is clearly established the impact of the noise strength and BM on the obtained W-shaped soliton. To determine the stability or instability zones, it was used the linear stability tool. It is shown that by varying the different parameters the Modulation bands can grow instability and stability zones can also emerge. These results permit to consolidate the previous works (Albosaily et al. in symmetry 12:1874, 2020, Abdelrahman et al. in AIMS Math 6:2970, 2021) exposed on the effects of noise on the soliton and the MI gain is new in this context. [ABSTRACT FROM AUTHOR]