Dispersive shock waves

Here are some graphical reprentations of the papers I have authored in. I'am currently interested in dispersive shock waves in fluid dynamics problems. The problems considered so far are KdV type equations.The shown below is the Gardner equation which is the KdV equation with an extra cubic term. This extra cubic term gives a much richer behaviour then the KdV case. The dispersive shock waves are produced using Whitham modulation theory. Whitham theory involves describing traveling wave solutions where the paramters change slowly during the length scale of the wavelength, the parameters are then described by the Whitham equations. The IVP for the Whitham equations are solved using matched regularisation introduced by Gurevich & Pitaevskii (1974) which involves solving a moving boundary problem see Scolarpedia for more details.

Here is a talk I have prepare on my Gardner work and an introduction into dispersive shock waves DSW talk