On abundant wave structures of the unsteady korteweg-de vries equation arising in shallow water
Kang‐Jia Wang, Jinghua Liu
Abstract
The aim of this paper is to study the unsteady korteweg-de vries equation that plays an important role in describing the shallow water. Two analytical techniques namely the Sardar-subequation method and the energy balance method are employed to seek the abundant traveling wave solutions for the first time. By these two methods, plenty of traveling wave solutions such as the bright solitary wave solutions, dark solitary wave solutions, singular periodic wave solutions and perfect periodic wave solution that expressed in terms of the generalized hyperbolic functions, generalized trigonometric functions and the cosine function are obtained. Finally, the dynamic behaviors of the solutions are described through the 3D plot and 2D curve. The results in this paper demonstrate that the proposed methods are powerful and effective to construct the traveling wave solutions of the nonlinear evolution equations in ocean engineering and science.