Soliton solutions of the three-component q-deformed KP equation

In this paper, we study the [Formula: see text]-deformation of the soliton solutions [Formula: see text], [Formula: see text] and [Formula: see text] of the three-component Kadomtsev–Petviashvili (KP) equation for different values of the parameter [Formula: see text] on the basis of the [Formula: see text]-KP hierarchy and the three-component KP equation. We obtain the soliton solutions of the three-component [Formula: see text]-KP equation and find that it agrees with the soliton solutions of the classical three-component KP equation when [Formula: see text]. Furthermore, the [Formula: see text]-solitons graph is shifted to the upper-left as [Formula: see text] decreases from 1 to 0 and does not change the structure of the [Formula: see text]-solitons, i.e. it does not change the number of the bright solitons and the dark solitons for [Formula: see text], [Formula: see text]. And when the number of [Formula: see text]-solitons in the solution is high and the value of the parameter terms [Formula: see text], [Formula: see text], [Formula: see text] is larger, the shape of the [Formula: see text]-soliton can differ significantly from the classical soliton solution, such as, the amplitude of the soliton and the position of intersection between [Formula: see text]-solitons. At the same time, we find that the closer the value of [Formula: see text] in the resulting analytical solution of the three-component [Formula: see text]-KP equation is to 0, the more it differs from the classical solution. This mathematical phenomenon can be described from the physical point of view as follows: the continuous process of [Formula: see text] value approaching to 0 from 1 corresponds to the continuous movement of the water wave from the original position (i.e. the graph of the classical solution).