This paper retrieves an optical 1–soliton solution to a model that is written as a concatenation of the Lakshmanan–Porsezian–Daniel model and Sasa–Satsuma equation. The method of undetermined coefficients obtains a full spectrum of 1–soliton solutions. The multiplier approach yields the conserved densities, which subsequently lead to the conserved quantities from the bright 1–soliton solution.

We consider the propagation of ultrashort solitons in noncentrosymmetric quadratically nonlinear optical media described by a general Hamiltonian of multilevel atoms. We use a long-wave approximation to derive a coupled system of Korteweg\char21{}de Vries equations describing ultrashort soliton evolution in such materials. This model was derived by using a rigorous application of the reductive perturbation formalism (multiscale analysis). The study of linear eigenpolarizations in the degenerate case and the corresponding formation of half-cycle solitons from few-cycle-pulse inputs are also presented.

We consider the propagation of circularly polarized few-cycle pulses (FCPs) in Kerr media beyond the slowly varying envelope approximation. Assuming that the frequency of the transition is far above the characteristic wave frequency (long-wave-approximation regime), we show that propagation of FCPs, taking into account the wave polarization, is described by the nonintegrable complex modified Korteweg\char21{}de Vries (cmKdV) equation. By direct numerical simulations, we get robust localized solutions to the cmKdV equation, which describe circularly polarized few-cycle-optical solitons and strongly differ from the breather soliton of the modified Korteweg\char21{}de Vries equation, which represents linearly polarized FCP solitons. The circularly polarized FCP soliton becomes unstable when the angular frequency is less than 1.5 times the inverse of the pulse length. The unstable subcycle pulses decay into linearly polarized half-cycle pulses, the polarization direction of which slowly rotates around the propagation axis.