Switch-On Shock applet:

===>Uses the Crank-Nicholson method to integrate the DNLSB.  Appears to be accurate and efficient.  Adjust the "Courant parameter", C = Dt/Dx, to take a bigger time step.  For C too big, numerical instability occurs.  

===>The dispersion, R, and dissipation, Rbar, can be adjusted through the applet interface.  The numerical result for the y-component of the magnetic field is in black and the x-comp. is in green.  This is plotted over the exact solution which has the y-comp. as dark gray and the x-comp. as dark green.  These seem to coincide well.

===>Included for starters is the simple perturbing effect "Gb" with G = Gr + Gi.  This  is set to zero by default.  A simple linear analysis shows Gr positive to lead to an exponential growth of the wave amplitude and Gi to lead to a faster wave speed.  Take values of these to be quite small ... ~ 0.001 or smaller.  Larger values quickly lead to a violation of the assumed boundary conditions.

===>Some things that might be interesting/amusing to check:  interaction of the S-O Shock with other waves, changing the numerical frame of reference to that of the shock, adding a periodic (or stochastic?) driver, seeing how the shock adapts if the dispersion or dissipation is adjusted (separately from the values which define the shock structure) ...