Application of symmetry analysis to viscoelastic fluid model

In the present paper, we apply Lie symmetry to the Suliciu relaxation system governed by viscoelastic shallow fluid. Utilizing the local symmetries of the governing PDEs, we derive the one-dimensional optimal system of subalgebras and construct several new exact solutions through symmetry reduction. Further, we employ the direct multipliers method to the given model to extract new conservation laws. Furthermore, we establish potential systems and inverse potential systems (IPS) to classify the nonlocal symmetry of the governing system. In addition, we develop some non-trivial exact solutions of the given model using the nonlocal symmetries of IPS. Finally, we investigate the propagation and interaction of C1-wave and characteristic shock.