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