Fig. 3

Cosh profile of delta spike. Comparison of a delta spike with a cosh profile of form (20). Note that the cosh profile shown here is not a best fit, but rather an analytically derived approximation, as discussed in the Appendix. The delta spike comes from a simulation with parameters ε=2.5e−6, dx=2.5e−4, and initial data u(x,0)= sin(2πx)+.1. Again, the positive and negative spikes must be added together to give the net weight of the delta shock