Doubly and Triply Periodic Waves Solutions for the KdV Equation

Abstract

Based on the arbitrary constant solution, a series of explicit doubly periodic solutions and triply periodic solutions for the Korteweg-de Vries (KdV) equation are first constructed with the aid of the Darboux transformation method.

Periodic and decay mode solutions of the generalized variable-coefficient Korteweg–de Vries equation

“…(1) through Bell polynomials method. 20,21 Recently, Huang 22 obtained the doubly and triply periodic solutions of the constantcoefficient KdV equation by using the Darboux transformation method. Wang 23 applied the nonlinear transformation leads to the 1-decay solution and the 2-decay mode solution of the constant-coefficient KdV equation.…”

“…When a 1 (t) = 6, a 2 (t) = 1, a 3 (t) = 0, Eq. (2) yields the standard KdV equation, 22,[26][27][28] i.e.…”