# Additional Material for Novikov Veselov Papers

For the paper **The Novikov-Veselov Equation: Theory and Computation**
by R. Croke, J.L. Mueller, M. Music, P. Perry, S. Siltanen and A. Stahel,
in Nonlinear Wave Equations, Contemporary Mathematics, vol. 635, Amer. Math. Soc., Providence, RI, 2015, pp. 25-70, we provide animations and
high resolution images for some of the figures
NVTheoryComputation.pdf.
- Figure 2. Evolution of a KdV ring by NV at zero energy
- Figure 3. Evolution of a KdV ring by NV at positive energy

This section contains additional information for the published papers
**The Novikov-Veselov Equation and the Inverse Scattering Method**
by Matti Lassas, Jennifer L Mueller, Samuli Siltanen and Andreas Stahel.
## The two papers

## Pictures and animations for part II: Computation

- Figure 1: Cross sectional plots for Example 1 and 2, low and high contrast:
gamma0Radial.eps,
q0Radial.eps.
- Figure 2: Cross sectional plots for Example 3:
gamma0Example3.eps,
q0Example3.eps
- Figure 3: Contour plots for real and imaginary part of the
scattering transform
- Animations for the real and imaginary part of the scattering
transform for Example 2, high contrast:
- Figure 4: Evolution of potential for Example 1, low contrast:
Radial1Init.eps
- Figure 5: Potential for Example 1 at t=0.001, low contrast:
Radial1.eps
- Animation for the NV evolution for Example 1, low contrast:
Radial1.avi
- Figure 5: Potential for Example 2 at t=0.001, high contrast:
Radial2.eps
- Animation for the NV evolution for Example 2, high contrast:
Radial2.avi
- Figure 6: Contour for Example 2 at t=0.001, high contrast:
Radial2Cont.eps
- Figure 7: Potential for Example 3 at t=0.001:
Example3.eps
- Animation for the NV evolution for Example 3:
- Figure 8: Difference ISM FD for Example 1 at t=0.001:
Radial1Difference.eps
- Figure 8: Difference ISM FD for Example 2 at t=0.001:
Radial2Difference.eps
- Figure 9: Difference ISM FD for Example 3 at t=0.001:
Example3Difference.eps

## Animations for the transversal instability paper

There are two animations for the paper
**Transverse instability of plane wave soliton solutions of the
Novikov-Veselov equation** by R. Croke, J.L. Mueller and
A. Stahel, in Nonlinear Wave Equations, Contemporary Mathematics,
vol. 635, Amer. Math. Soc., Providence, RI, 2015, pp. 71-89
NVStability.pdf
- First the traveling wave solution, with a slowly growing perturbation:
solution.avi
- Then the difference to a pure KdV traveling soliton:
difference.avi.
Observe that the difference is moving and growing exponentially,
without changing shape.

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Andreas Stahel