Zhang, Jinliang; Wang, Fei A similarity transformation and the decay mode solutions for three-dimensional cylindrical Kadomtsev-Petviashvili equation. (English) Zbl 1438.35382 Math. Appl. 32, No. 2, 370-375 (2019). Summary: In this paper, a similarity transformation between the solutions of three-dimensional cylindrical Kadomtsev-Petviashvili equation and the solutions of three-dimensional Kadomtsev-Petviashvili equation with constant coefficients is firstly derived, and the corresponding constraint conditions for the coefficients of the three-dimensional cylindrical Kadomtsev-Petviashvili equations are obtained. Then the exact solutions of the three-dimensional cylindrical Kadomtsev-Petviashvili equation are expressed by the similarity transformation and the solutions of the three-dimensional Kadomtsev-Petviashvili equation with constant coefficients. Lastly, four special three-dimensional cylindrical Kadomtsev-Petviashvili equations are studied, especially, the decay mode solutions of these three-dimensional cylindrical Kadomtsev-Petviashvili equations are obtained. MSC: 35Q53 KdV equations (Korteweg-de Vries equations) Keywords:three-dimensional cylindrical Kadomtsev-Petviashvili equation; similarity transformation; decay mode solution PDFBibTeX XMLCite \textit{J. Zhang} and \textit{F. Wang}, Math. Appl. 32, No. 2, 370--375 (2019; Zbl 1438.35382)