Videos

 
Korteweg-de Vries equation

One dimensional wave phenomena in the long wave-length limit, for instance waves in shallow water (see e.g. nlin/0512066 and references therein).


Solitons and almost periodic solutions (nlin/0512066)

2-soliton solution

Hyperelliptic solution, genus 2

Hyperelliptic solution, genus 6


Small dispersion limit (99/2005)

KdV solution for hump-like initial data in the small dispersion limit

Low-dispersion KdV

Low-dispersion KdV (zoom)

KdV + asymptotic solution (Whitham)

Difference KdV-asymptotic solution (Whitham)


Kadomtsev-Petviashvili equation
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Essentially one dimensional wave phenomena in the long wave-length limit with weak transversal effects, for instance waves in shallow water (see e.g. 124/2005 and references therein).


Solitons and almost periodic solutions (nlin/0512066,124/2005)

KP line 2-soliton

KP line 4-soliton

KP, perturbed line soliton

Hyperelliptic KP solution, genus 2

Hyperelliptic KP solution, genus 4


Small dispersion limit (124/2005)

KP solution for initial data with compact support in the low dispersion limit

Low dispersion KP, small data

Low dispersion KP solution (0.1)

Low dispersion KP solution (0.01)


Davey-Stewartson equation


Amplitude modulation of weakly two dimensional waves, for instance waves in shallow water (see e.g. 124/2005 and references therein).

DS solution (absolute value)


Ernst equation

Equivalent to the stationary axisymmetric Einstein equations in vacuum. Solutions describe the gravitational field of black holes (correspond to solitonic solutions) and stars and galaxies in thermodynamical equilibrium (see e.g. LN 29/2006 and references therein).

Hyperelliptic disk solution (real part)

Hyperelliptic disk solution (imaginary part)