Xo
Yo
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-8 ≤ Xo,Yo ≤ 8.
You see m=2 vertex decay into two m=1 vorteces (in a while :)
2D vortex dynamics
Nonlinear wave equation
∂t2u = Δu +
(1 - |u|2)u with complex u has stationary vortex solutions with the integer
winding numbers m of the form
um(r) = Am(r)
exp(imθ).
It is known [1] that the m = 1 vortices are stable and m ≥ 2
vortices are unstable. In this CPU based simulation you see m=2 vertex
decay. Explicit scheme is used on a 250x250 grid. A simple approximation
(the dashed curve) is used for the initial m=2 vertex.
|u(x,y)| is plotted. Colors correspond to the u phase.
[1] "Quantized vortex stability and interaction in the nonlinear
wave equation"Weizhu Bao, Rong Zengc,
Yanzhi Zhang.
