ABSTRACT
This chapter examines the dynamics of optical solitons with power law nonlinearity and a generalization of Kerr law nonlinearity. It discusses the physics of power law nonlinearity and the mathematical issues of the nonlinear Schrodinger’s equation (NLSE) with power law nonlinearity. The chapter reviews the three conserved quantities of the NLSE with power law nonlinearity. It also discusses the adiabatic parameter dynamics of the solitons with power law due to the presence of perturbation terms. The chapter explores the quasi-stationarity aspect of the perturbed NLSE with power law nonlinearity. Power law nonlinearity is exhibited in various materials, including semiconductors. This law also occurs in media for which higher order photon processes dominate at different intensities. Moreover, in nonlinear plasmas, the power law solves the problem of small-K condensation in weak turbulence theory.
