Various localized nonlinear wave structures in the (2 + 1)-dimensional KdV system

Abstract

Korteweg–de-Vries (KdV) equation has many applications such as in the description of shallow water waves and ion-acoustic waves in plasmas. In this paper, we investigate the novel nonlinear wave structures in the [Formula: see text]-dimensional KdV system. Starting from the [Formula: see text]-soliton solution of the [Formula: see text]-dimensional KdV system, some new interaction phenomena of line soliton, breather soliton and lump soliton are found based on the Hirota bilinear method and the long wave limit method. The interaction processes of such solutions are shown graphically to display the novel nonlinear structures in this system. These interesting phenomena in this work could be helpful for understanding certain physical phenomena in nonlinear optics and relevant fields.