Our group studies the dynamics of optical solitons in presence of higher order dispersions by the aid of He’s semi-inverse variational principle. Both Kerr law and power law nonlinearity are taken into account. A closed form analytical soliton solution has been obtained along with numerical simulations that supports the analytical study.
Soliton perturbation theory is being studied for classical solitons with full nonlinearity. There are five types of nonlinear media that are considered. They are Kerr law, power law, parabolic law, dual-power law and the log law. In presence of dispersive perturbation terms, the phenomena of optical soliton cooling is also observed. This study will be extended to the case of carrying out the integration of the governing equation by the aid of multiple-scale perturbation analysis.
Finally the governing equation is being studied with time-dependent coefficients of dispersion, nonlinearity and perturbation terms. In some special cases an exact soliton solution has been obtained, including dark solitons. These results are all supported by numerical simulations.