A new note on exact complex travelling wave solutions for (2+1)-dimensional B-type Kadomtsev-Petviashvili equation

Exact solutions of the (2+1) – dimensional Kadomtsev – Petviashvili by Zhang [Zhang H., Applied Mathematics and Computation 216 (2010) 2771 – 2777] are considered. To look for ”new types of exact solutions travelling wave solutions” of equation Zhang has used the G’/G – expansion method. We demonstrate that there is the general solution for the reduction by Zhang from the (2+1) – dimensional Kadomtsev – Petviashvili equation and all solutions by Zhang are found as partial cases from the general solution. In recent paper [1] author has looked for exact solutions of the system of equations uy = qx vx = qy qt = qxxx + qyyy + 6 (q u)x + 6 (q v)y (1) where u ≡ u(x, y, t), v ≡ v(x, y, t) and q ≡ q(x, y, t) are dependent variables with respect to x, y and t. Zhang [1] looked for exact solutions of Eq.(1) using the travelling wave solutions taking into account the following variables q(x, y, t) = q(z), u(x, y, t) = u(z), v(x, y, t) = v(z), z = i(α x + β y + c t). (2) As result he obtained the system of equations in the form