Negative-order KdV equations in (3+1) dimensions by using the KdV recursion operator

We develop a variety of negative-order Korteweg-de Vries (KdV) equations in (3 + 1)-dimensions. The recursion operator of the KdV equation is used to derive these higher dimensional models. The new equations give distinct solitons structures and distinct dispersion relations as well. We also determine multiple soliton solutions for each derived model.