Breather Wave and Traveling Wave Solutions for A (2 + 1)-Dimensional KdV4 Equation

Abstract

In this paper, an integrable (2 + 1)-dimensional KdV4 equation is considered. By considering variable transformation and Bell polynomials, an effective and straightforward way is presented to derive its bilinear form. The homoclinic breather test method is employed to construct the breather wave solutions of the equation. Then, the dynamic behaviors of breather waves are discussed with graphic analysis. Finally, the $\left(G^{\prime }/G^2\right)$ expansion method is employed to obtain traveling wave solutions of the (2 + 1)-dimensional integrable KdV4 equation, including trigonometric solutions and exponential solutions.