Conservation laws, nonlocal symmetries, and exact solutions for the Cargo–LeRoux model with perturbed pressure

In this study, we have formulated conservation laws for the Cargo–LeRoux model by utilizing both the direct multiplier technique and nonlinear self-adjointness. These conservation laws include a perturbed state pressure equation. Using conservation laws, we have demonstrated a methodology for generating explicit solutions for nonlinear partial differential equations and verified its effectiveness using the local conservation laws specific to the Cargo–LeRoux model. Our investigation indicates that these conservation laws yield solutions distinct from those obtained through group invariance methods. Moreover, we have established a comprehensive framework for constructing a network of partial differential equations which are nonlocally related to the governing system. This network includes systems derived from local conservation laws and symmetry methods. Additionally, we have classified the nonlocal symmetries arising from these potential systems and applied them to discover exact solutions for the Cargo–LeRoux model.