Dispersive shock waves

    KdV Dispersive shock wave:
    Here is a typical demonstration of a dispersive shock produced by nonlinear wave breaking with a initial hump condition
    the animation is the numerical solution of the kdV equation with small dispersion term as shown with a hump like
    initial condition.
    

Shock Fitting:

Here is a illustration of a shock being fitted at the point of wave breaking.
The shock is fitted using a method outlined in Whitham (1974). A chord is made so
it cuts lobes of equal area.
	    

Burgers Equation:

Here is a numerical solutions of the burgers equation with a hump initial profile.The behaviour is very different from the dispersive case.
However it is very like the shock fitting case which suggests that the viscosity term naturally fits a shock.