The novel KdV model plays a significant part in the discovery of a variety of nonlinear ion acoustic wave and harmonic crystal phenomena. The new homoclinic method based on the Hirota bilinear form is used to create the bilinear form of the new KdV equation and uncover numerous new exact solu tions. The stability of the solutions is studied in this article using the modulation instability. The results show novel mechanical structures and new properties for this evolution equation. The physical dynamics of the traveling wave solutions produced by the recently suggested homoclinic approach to reinforce the Hirota bilinear method are investigated, the obtained solutions are represented using 2?dimensional, 3?dimensional and contour plots. To guarantee their existence, all the solutions that have been found are inserted into the model. These results open up a new opportunity for us to thoroughly investigate the model. Numerous exciting physical occurrences in the fields of shallow-water waves, ion-acoustic waves in plasma, acoustic waves in harmonic crystal and other related phenomena are reported using the existing work on a regular basis