Soliton dynamics for a nonintegrable model of light-colloid interactive fluids

A nonintegrable model with the super-Kerr nonlinearity is investigated, which describes the light-matter interactions in a fluidic suspension of colloidal nanoparticles. Existence of the solitons with semi-analytic forms is shown for this model via the variational method. Numerical simulation is performed to demonstrate the good accordance with the variational analysis. Soliton interactions and soliton bound states are discussed in both the homogeneous and inhomogeneous media. In particular, inelastic interactions of two solitons are presented, and we find that there is an energy distribution P±\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_\pm $$\end{document}, which has a dependence with the velocity of the high-energy solitons. Simulations also reveal that the maximum value of P-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$P_-$$\end{document} relates with the soliton energy and the model parameter β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}. Moreover, two different patterns of the three-soliton interactions are depicted as manifestation of the nonintegrability.