Korteweg–De Vries hierarchy

In mathematics, the Korteweg–De Vries (KdV) hierarchy is an infinite sequence of mutually compatible nonlinear evolution equations containing the Korteweg–de Vries equation as its first nontrivial member. It is one of the central examples in the theory of integrable systems and soliton equations, because it combines several characteristic features of integrability: a Lax formulation, infinitely many commuting flows and conserved quantities, Hamiltonian and bi-Hamiltonian structures, and exact solution methods such as the inverse scattering transform and finite-gap integration.

Source: Wikipedia — Korteweg–De Vries hierarchy (CC BY-SA 4.0)