Colloidal solitary waves with temperature dependent compressibility

Spatial solitary waves which form in colloidal suspensions of dielectric nanoparticles are considered. The interactions, or compressibility, of the colloidal particles, is modelled using a series in the particle density, or packing fraction, where the virial, or series, coefficients depend on the type of particle interaction model. Both the theoretical hard disk and sphere repulsive models, and a model with temperature dependent compressibility, are considered. Experimental results show that particle interactions can be temperature dependent and either repulsive or attractive in nature, so we model the second virial coefficient using a physically realistic temperature power law. One- and two-dimensional semi-analytical colloidal solitary wave solutions are found. Trial functions, based on the form of the nonlinear Schrödinger equation soliton, are used, together with averaging, to develop the semi-analytical solutions. When the background packing fraction is low, the one-dimensional solitary waves have three solutions branches (with a bistable regime) while the two-dimensional solitary waves have two solution branches, with a single stable branch. The temperature dependent second virial coefficient results in changes to the solitary wave properties and the parameter space, in which multiple solutions branches occur. An excellent comparison is found between the semi-analytical and numerical solutions.