Dynamics of multi-solitons, multi-lumps and hybrid solutions in (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation

Abstract

The (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani (KdVSKR) equation is proposed by extending one dimension of the (1+1)-dimensional KdVSKR equation. The bilinear form of the (2+1)-dimensional KdVSKR equation is obtained by the independent transformation. The multi-solitons are obtained by solving the Hirota bilinear form of the (2+1)-dimensional KdVSKR equation. By using the long wave limit method, the multi-order lumps, interaction between lump and solitons are derived. The paths of lump wave can be given by calculating the critical points of the lump wave. The dynamics of these solutions are shown both in numerical simulations and graphs ways.

Keywords

• (2+1)-dimensional Korteweg–de Vries–Sawada–Kotera–Ramani equation
• Hirota bilinear method
• Long wave limit
• Lump