Movies of Nonlinear Dispersion on a Periodic Domain

Movies created by Gong Chen.   For detailed explanation and discussion, see:

  • Chen, G., and Olver, P.J., Dispersion of discontinuous periodic waves, Proc. Roy. Soc. London A 469 (2012), 20120407.   pdf

    Korteweg--deVries equation:     ut = - uxxx + u ux

    Solution with step function initial data at   t = 0.

    Δ t = .0001 π

     

    Δ t = .001 π

     

    Korteweg--deVries equation:     ut = - .00484 uxxx - u ux

    Zabusky-Kruskal solution with cosine initial data at   t = 0.