The mathematical and wave profile analysis of the Maccari system in nonlinear physical phenomena

The two-dimensional nonlinear complex coupled Maccari system is a significant model in optics, quantum mechanics, plasma physics, hydrodynamics and some other fields. In this article, we have investigated scores of broad-spectral soliton solutions to the stated system via the auxiliary equation technique. The obtained solutions are established as an integration of the rational function, hyperbolic function, trigonometric function and exponential function. We have portrayed the three- and two-dimensional combined structures of the obtained solutions for a better interpretation of the waves, and it is determined that λ is the most effective and influential parameter that significantly affects the change in wave type, as shown in the 2D figure. The effects of other parameters have also been discussed. The numerical results show that the approach is reliable, straightforward and potent to examine other nonlinear evolution equations that emerged in optics, nonlinear physics, applied mathematics, and engineering.