Various exact wave solutions for KdV equation with time-variable coefficients

Abstract

In this study, we investigate the (2 + 1)-dimensional Korteweg-De Vries (KdV) equation with the extension of time-dependent coefficients. A symbolic computational method, the simplified Hirota’s method, and a long-wave method are utilized to create various exact solutions to the suggested equation. The symbolic computational method is applied to create the Lump solutions and periodic lump waves. Hirota’s method and a long-wave method are implemented to explore single-, double- and triple-M-lump waves, and interaction physical phenomena such as an interaction of single-M-lump with one-, two-soliton solutions, as well as a collision of double-M-lump with single-soliton waves. Furthermore, the simplified Hirota’s method is employed to explore complex multi-soliton solutions. To realize dynamics, the gained solutions are drawn via utilizing different arbitrary variable coefficients.

Keywords

• Hirota’s method
• Lump solutions
• Interaction phenomena
• Complex multi-soliton waves
• KdV equation