Derivation of a modified Korteweg–de Vries model for few-optical-cycles soliton propagation from a general Hamiltonian

Propagation of few-cycles optical pulses in a centrosymmetric nonlinear optical Kerr (cubic) type material described by a general Hamiltonian of multilevel atoms is considered. Assuming that all transition frequencies of the nonlinear medium are well above the typical wave frequency, we use a long-wave approximation to derive an approximate evolution model of modified Korteweg–de Vries type. The model derived by rigorous application of the reductive perturbation formalism allows one the adequate description of propagation of ultrashort (few-cycles long) solitons.