Conservation laws, exact solutions and nonlinear dispersion: A lie symmetry approach

In this study, we investigated a set of equations that exhibit compact solutions and nonlinear dispersion. We used the classical lie symmetry approach to derive ordinary differential equations (ODEs) that are well suited for qualitative study. By examining the dynamic behavior of these ODEs, we gained insights into the intricate nature of the underlying system. We also used a powerful multiplier approach to establish nontrivial conservation laws and exact solutions for these equations. These conservation laws provide essential information regarding the underlying symmetries and invariants of the system, and shed light on its fundamental properties.