General soliton and (semi-)rational solutions to the y-non-local Mel’nikov equation with non-zero boundary conditions are derived by the Kadomtsev–Petviashvili (KP) hierarchy reduction method. The solutions are expressed in N × N Gram-type determinants with an arbitrary positive integer N. A possible new feature of our results compared to previous studies of non-local equations using the KP reduction method is that there are two families of constraints among the parameters appearing in the solutions, which display significant discrepancies. For even N, one of them only generates pairs of solitons or lumps while the other one can give rise to odd numbers of solitons or lumps; the interactions between lumps and solitons are always inelastic for one family whereas the other family may lead to semi-rational solutions with elastic collisions between lumps and solitons. These differences are illustrated by a thorough study of the solution dynamics for N = 1, 2, 3. Besides, regularities of solutions are discussed under proper choices of parameters.

用Kadomtsev–Petviashvili（KP）层次化约简方法推导了具有非零边界条件的y非局部Mel'nikov方程的一般孤子解和（半）理性解。解以具有任意正整数N的N × N Gram型行列式表示。与以前使用KP约简方法进行的非局部方程式研究相比，我们的结果的一个可能新特征是，解决方案中出现的参数之间存在两个约束条件，这显示出明显的差异。连N，其中一个仅生成一对孤子或块，而另一对则产生奇数个孤子或块；块和孤子之间的相互作用对于一个家庭总是无弹性的，而另一个家庭可能导致块与孤子之间发生弹性碰撞的半理性解。这些差异是由于在溶液动力学研究透彻所示Ñ = 1，2，3。此外，溶液的规律被下的参数适当选择所讨论的。