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

In this paper, we study the q-deformation of the soliton solutions u(0q), u(1q), and u(2q) of the three-component Kadomtsev-Petviashvili (KP) equation for different values of the parameter q on the basis of the q-KP hierarchy and the three-component KP equation. We obtain the soliton solutions of the three-component q-KP equation and find that it agrees with the soliton solutions of the classical three-component KP equation when q -> 1. Furthermore, the q-solitons graph is shifted to the upper-left as q decreases from 1 to 0 and does not change the structure of the q-solitons, i.e. it does not change the number of the bright solitons and the dark solitons for y >> 0, y << 0. And when the number of q-solitons in the solution is high and the value of the parameter terms x, (1-q)(i)/i(1-q(i))x(i), i = 2, 3 is larger, the shape of the q-soliton can differ significantly from the classical soliton solution, such as, the amplitude of the soliton and the position of intersection between q-solitons. At the same time, we find that the closer the value of q in the resulting analytical solution of the three-component q-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 q 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).