This article investigates the existence theory, exact solutions, and the unique solutions of physical problems. In this study the well-known Selkov–Schnakenberg system of coupled nonlinear unidirectional PDEs is analyzed. This is a simple chemical reaction system that admits periodic solutions. The existence of the system is extracted by applying contraction and self-mapping conditions. The new families of exact solutions which represent the concentration and chemical reactants in different forms are formulated. The periodic, singular periodic, shock wave, singular wave, and complex solitary-shock, shock-singular, double singular, and periodic-singular solutions are successfully extracted by using the new modified extended direct algebraic (MEDA) technique. Additionally the unique problems with corresponding proposed auxiliary data are discussed. The trends of these solutions are also sketched in different plots.

本文研究物理问题的存在论、精确解和唯一解。在这项研究中，分析了著名的耦合非线性单向 PDE 的 Selkov-Schnakenberg 系统。这是一个允许周期解的简单化学反应系统。通过应用收缩和自映射条件提取系统的存在性。制定了代表浓度和不同形式的化学反应物的新的精确解族。使用新的改进的扩展直接代数 (MEDA) 技术成功提取了周期解、奇异周期解、激波解、奇异波解和复孤激波、激波奇异解、双奇异解和周期奇异解。此外，讨论了相应建议的辅助数据的独特问题。