Circular dispersive shock waves in colloidal media

A dispersive shock wave (DSW), with a circular geometry, is studied in a colloidal medium. The colloidal particle interaction is based on the repulsive theoretical hard sphere model, where a series in the particle density, or packing fraction is used for the compressibility. Experimental results show that the particle interactions are temperature dependent and can be either repulsive or attractive, so the second term in the compressibility series is modified to allow for temperature dependent effects, using a power-law relationship. The governing equation is a focusing nonlinear Schrödinger-type equation with an implicit nonlinearity. The initial jump in electric field amplitude is resolved via a DSW, which forms before the onset of modulational instability. A semi-analytical solution for the amplitude of the solitary waves in a DSW of large radius, is derived based on a combination of conservation laws and geometrical considerations. The effect of temperature and background packing fraction on the evolution of the DSW and the amplitude of the solitary waves is discussed and the semi-analytical solutions are found to be very accurate, when compared with numerical solutions.