2+1 KdV(N) Equations

TL;DR

This paper introduces 2+1 dimensional nonlinear PDEs derived from the KdV equation, highlighting their shared 3-soliton solutions, similar structures, and passing the Painlevé test, indicating integrability.

Contribution

It derives new 2+1D PDEs from the KdV equation, analyzes their soliton structures, and demonstrates their integrability through the Painlevé test.

Findings

All equations have the same 3-soliton structures.

Solutions differ only in dispersion relations.

Equations pass the Painlevé test, indicating integrability.

Abstract

We present some nonlinear partial differential equations in 2+1-dimensions derived from the KdV Equation and its symmetries. We show that all these equations have the same 3-soliton structures. The only difference in these solutions are the dispersion relations. We also showed that they pass the Painlev\'e test.