(2 + 1)-dimensional Korteweg–de Vries (N) equations derived by using the Korteweg–de Vries recursion operator

Abstract

A new variety of (2 + 1)-dimensional Korteweg–de Vries (KdV(N)) equations with even distinct orders is developed. The recursion operator of the KdV equation is used to derive these equations. This study shows that these new equations possess multiple soliton solutions that are the same as the multiple soliton solutions of the KdV hierarchy, but differ only in the dispersion relations. Finally, we establish a generalization for the dispersion relations of these equations.