Three‐dimensional Korteweg‐de Vries equation and traveling wave solutions

Abstract

Abstract. The three-dimensional power Korteweg-de Vries equation [u t +u n u x +u xxx ] x + u yy + u zz = 0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave solutions for n = 1 and n = 2 are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.

The Modified Kudryashov Method for the Conformable Time Fractional (3+1)-dimensional Kadomtsev-Petviashvili  and the Modified Kawahara Equations

“…The solitary waves of the three-dimensional KP equation both are in cylindrical form for the transverse variables and decay with algebraically optimal rate [9]. Beside the existence of the solitary wave solutions, the three-dimensional KP equation has cnoidal wave solutions to be written as infinite sum of solitons [10] and traveling wave solutions to be expressed in the form of hyperbolic, rational and trigonometric functions [11].…”