Multi-soliton solutions of Ito-type coupled KdV equation with conservation laws in Darboux framework

In this paper, we derive the Darboux solutions of Ito-type coupled KdV equation in Darboux framework which is associated with Hirota Satsuma systems. One of the main results is the generalization of Nth-fold Darboux solutions in terms of Wronskians. We also derive the exact multi-soliton solutions for the coupled field variables of that system in the background of zero seed solutions. With the addition of these findings, we also enrich our results with the graphical interpretations of interacting solitons which preserve their profiles after the collision as usually solitons possess such property intrinsically. Subsequently, we construct the equation of continuity that yields the infinite conserved quantities associated with interacting phenomenon of multi-solitons.