Folding sheets are a form of soliton

1. Folding sheets are a form of soliton Ka Yee C. Lee, University of Chicago, DMR 0820054 How a pendulum soliton is related to a buckled sheet. Connected pendulums at left are swinging in a "breather" mode, a form of soliton. It remains localized in space because of its high swings. Height of the surface under the pendulums shows their swing angles. Surface extends to the right to show the time-dependence of the swinging pattern. The diagonal edge is accentuated. Red curve is drawn to have its slope-angle at each point equal to the swing angle along the edge. This curve has the shape of a film floating on a liquid compressed so that it buckles and folds [1]. Black tie-lines indicate corresponding points on the two curves. Below the red line is a photo of a thin plastic film 6 cm long floating on a trough of water, viewed edge-on, from [2]. MRSEC scientists and collaborators have shown[1] that the localized buckling of a compressed thin sheet, important for molecular interfaces, [2] has the same mathematical origin as the localization of kinetic energy in a line of swinging pendulums. It is a form of soliton. [1]* HaimDiamant and Thomas A. Witten, Physical Review Letters, 107 164302 (2011). [2]* Pocivavsek et al, Science 16 May 2008: 320 912-916