Neuberger, Rice, and Swift paper

Numerical Solutions of a Vector Ginzburg-Landau Equation with a Triple Well Potential

by John M. Neuberger, Dennis R. Rice Jr., and James W. Swift

International Journal of Bifurcation and Chaos, vol. 13, no. 11 (2003) pp. 3295-3306.

Solutions to the ODE -eps^2 u'' + W'(u) = 0, W(u) = 1/4 - u^2/2 + u^4/4, u'(0) = u'(1) = 0, using 20 Fourier Modes:
animation and still.

Figure 1. (The Triple Well Potential)
The Upside-Down Triple Well Potential.
Figure 2. (Bifurcation Diagram)
Figure 3. (Solutions)
Figure 4. (Conjectured solutions at J = 0)
Figure 5. (Adding more Modes)
Figure 6. (Error)

Preprint of the paper.

Animations of Solutions

Triple Junction on the Disk (From John M. Neuberger.)

    Jim Swift's home page     Department of Math/Stat     NAU