The deformed modified Korteweg–de Vries equation: Multi-soliton solutions and their interactions

Abstract

In this paper, we demonstrate how Hirota’s bilinear method can be employed to derive single-soliton, two-soliton and three-soliton solutions of the deformed modified Korteweg–de Vries (KdV) equation. We note that the derived soliton solutions depend on the time-dependent function, revealing that the speed of the soliton solutions no longer explicitly depends on wave amplitude. Finally, we graphically demonstrate the evolution of multi-soliton solutions and their interactions.