Symmetry reductions and conservation laws of a modified-mixed KdV equation: exploring new interaction solutions

This article represented the investigation of the modified mixed Korteweg-de Vries equation using different versatile approaches. First, the Lie point symmetry approach was used to determine all possible symmetry generators. With the help of these generators, we reduced the dimension of the proposed equation which leads to the ordinary differential equation. Second, we employed the unified Riccati equation expansion technique to construct the abundance of soliton dynamics. A group of kink solitons and other solitons related to hyperbolic functions were among these solutions. To give the physical meaning of these theoretical results, we plotted these solutions in 3D, contour, and 2D graphs using suitable physical parameters. The comprehend outcomes were reported, which can be useful and beneficial in the future investigation of the studied equation. The results showed that applied techniques are very useful to study the other nonlinear physical problems in nonlinear sciences.