Infinitely Many Lax Pairs of the Korteweg-de Vries Equation

Starting from a known Lax pair, one can get some infinitely many coupled Lax pairs.In this letter, we take the well-known KdV equation as a typical example. Using infinitely many symmetries, the infinitely many inhomogeneous linear Lax pairs of KdV equation can be obtained. And considering the Darboux transformations for the KdV equation leads to the infinitely many inhomogeneous nonlinear Lax pairs.