  The Novikov-Veselov (NV) equation is a dispersive (2+1)-dimensional nonlinear
evolution equation that generalizes the (1+1)-dimensional Korteweg-deVries
(KdV) equation. This paper considers the stability of plane wave soliton
solutions of the NV equation to transverse perturbations. To investigate the
behavior of the perturbations, a hybrid semi-implicit/spectral numerical scheme
was developed, applicable to other nonlinear PDE systems. Numerical simulations
of the evolution of transversely perturbed plane wave solutions are presented.
In particular, it is established that plane wave soliton solutions are not
stable for transverse perturbations.
