Unraveling Symmetry Properties in a Three-Dimensional Nonlinear Evolution Model via the Lie Group Method

This research focuses on a (3+1)-dimensional nonlinear evolution model originating from the Jaulent-Miodek hierarchy. Several tools can be used to examine the symmetry of the model. However, our primary emphasis lies in harnessing one of the most significant and powerful analytical tools available for this purpose: the Lie group method. The Lie group method is an effective approach for uncovering the symmetry properties inherent in a model and exploring group-invariant solutions using symmetry algebra. In addition, we applied Ibragimov's method to study conservation laws relevant to the considered model. Our study is significant as it contributes to the investigation of this model and addresses a particular gap in the group-theoretic approach in this context. Our findings represent novel contributions to the study of the model under consideration.