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 $N$th-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.

本文在与 Hirota Satsuma 系统相关的 Darboux 框架中推导了 Ito 型耦合 KdV 方程的 Darboux 解。主要结果之一是根据 Wronskians 推广 $N$ 倍 Darboux 解。我们还在零种子解的背景下推导了该系统耦合场变量的精确多孤子解。除了这些发现之外，我们还通过相互作用的孤子的图形解释丰富了我们的结果，这些孤子在碰撞后保留了它们的轮廓，因为通常孤子本质上具有这种性质。随后，我们构建了连续性方程，产生与多孤子相互作用现象相关的无限守恒量。