Korteweg-de Vries equation with finite-gap boundary conditions, and the Whitham deformations of Riemann surfaces (Q753025)

The Cauchy problem is considered for the KdV equation with the initial data tending quickly to their asymptotic values, and the behaviour of its solution is described as \(t\to +\infty\). The latter asymptotics is found to represent a Whitham deformation with no creation or annihilation of spectral zones. The solution involves a specific choice of the Whitham path and phase shift.