A new (2+1)-dimensional Korteweg–de Vries equation and its extension to a new (3+1)-dimensional Kadomtsev–Petviashvili equation

In this work, a recently developed (2+1)-dimensional Korteweg–de Vries (KdV) equation is studied. A new (3+1)-dimensional Kadomtsev–Petviashvili equation, which is an extension of the new KdV equation, is developed and examined as well. Multiple soliton solutions are determined for each equation. The conditions for the existence of multiple soliton solutions are established. The resonance phenomenon does not exist for any of the newly derived equations.