Exploring complex phenomena in fluid flow and plasma physics via the Schrödinger-type Maccari system

The nonlinear coupled Maccari system of the Schrödinger equation type is an important equation that covers a wide range of topics in fluid flow, deep-water wave theory, plasma physics, nonlinear optics, etc. This system is a non-linear model that describes the dynamics of isolated waves, confined in a small part of space. In the present work, we utilize the modified Jacobi elliptic expansion scheme and the new extended hyperbolic function method to obtain soliton solutions for the Maccari system. By performing certain procedures of wave variable alteration, the proposed system of nonlinear equations becomes a single-variable differential equation. Subsequently, several precise soliton solutions were recovered by effectively applying the proposed procedures. The solutions achieved are represented in 2D and 3D plots by appropriately allocating values to the associated unknown constants. These graphical representations help researchers to understand the fundamental mechanisms of complex occurrences using leading equations. Dynamical features such as phase portraits, quasi-periodic and chaotic behavior, and sensitivity analysis have been well explored. The approaches utilized exhibit commendable individual performances, which warrants their continued application in solving numerous other nonlinear evolution equations emerging in diverse scientific and engineering domains.