Novikov–Veselov equation

In mathematical physics, the Novikov–Veselov equation (or Veselov–Novikov equation) is a nonlinear partial differential equation. It is a two-dimensional analogue of the well-known Korteweg–de Vries equation (KdV equation), which can model shallow water waves. A key feature of the Novikov–Veselov equation is its integrability, meaning it can be solved exactly through a method known as the inverse scattering transform.

The equation's integrability is linked to the two-dimensional stationary Schrödinger equation, just as the KdV equation's integrability is linked to the one-dimensional Schrödinger equation. This property distinguishes it from other two-dimensional analogues of the KdV equation, such as the Kadomtsev–Petviashvili equation. The equation is named after Soviet mathematicians Sergei P. Novikov and A.P. Veselov, who introduced it in Novikov & Veselov (1984).

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