The Novikov--Veselov equation and the inverse scattering method: II. Computation

The Novikov–Veselov (NV) equation is a (2 + 1)-dimensional nonlinear evolution equation generalizing the (1 + 1)-dimensional Korteweg–deVries equation. The inverse scattering method (ISM) is applied for numerical solution of the NV equation. It is the first time the ISM is used as a computational tool for computing evolutions of a (2 + 1)-dimensional integrable system. In addition, a semi-implicit method is given for the numerical solution of the NV equation using finite differences in the spatial variables, Crank–Nicolson in time, and fast Fourier transforms for the auxiliary equation. Evolutions of initial data satisfying the hypotheses of part I of this paper are computed by the two methods and are observed to coincide with significant accuracy.