From Korteweg-de Vries to Novikov-Veselov, and back
The Novikov-Veselov (NV) equations are a 2+1 dimensional generalization of the Korteweg-de Vries (KdV) equation. Using the additional space dimension solutions to NV exhibit a rich variety of behavior, and thus mathematical challenges. The close connection between planar solutions to NV and solutions to KdV is presented.
Using the K-expansion method the instability of a planar soliton of NV is examined. Using a spectral method the analytical results are illustrated by numerical simulations.