Rigorous construction and classification of solitary-waves and exact soliton configurations in the nonlinear coupled Maccari system

The nonlinear coupled Maccari system, which is closely related to the Schrödinger equation, plays an important role in the modeling of nonlinear wave phenomena in areas such as deep-water wave theory, fluid dynamics, nonlinear optics, and plasma physics. In this work, the generalized exponential rational function (GERF) method is employed to derive traveling-wave and soliton solutions of the Maccari system. By introducing suitable wave-variable transformations, the governing nonlinear partial differential equations (PDEs) are reduced to ordinary differential equations (ODE) with respect to a single independent variable. The resulting analysis yields several classes of exact solutions, including non-topological and topological solitons, as well as exponential, kink-type, and periodic singular wave structures. These solutions contribute to a deeper understanding of the dynamical features represented by the Maccari system. The results further indicate that the GERF method provides a systematic analytical framework for constructing exact solutions of certain nonlinear evolution equations arising in applied mathematics and related scientific fields.