Soliton solutions of coupled resonant Davey-Stewartson system and modulation instability analysis

Abstract

In this paper, coupled resonant Davey-Stewartson (CRDS) system is studied. The resonant concept is quite important in fluid dynamics, magneto-acoustic waves and plasma physics. CRDS system models the two-wave propagation with periodic wave patterns and short-long wave propagation. Our primary aim is obtaining soliton solutions of this important CRDS system via generalized F-expansion method (GFEM) and auxiliary equation method (AEM). As a result of the application of the aforementioned methods to the model, soliton solutions both known in the literature and a rare type have been obtained. We obtained dark, bright, periodic-singular, two-dark and two-bright soliton solutions. Also, two-dark and two-bright soliton solutions are quite rare soliton types according to the literature research. The 3D and contour graphics of the obtained soliton solutions were drawn. On the other hand, we did modulation instability (MI) analysis on obtained solutions and according to the MI analysis, obtained results are clearly stable. As far as we know, the relevant methods were applied for the first time to this model. Again, modulation instability analysis was performed on the model for the first time. Therefore, the study includes innovative reviews and conclusions.