Propagation of an ultimately short electromagnetic pulse in a nonlinear medium described by the fifth-order Duffing model

We discuss propagation of an ultimately short (single-cycle) pulse of an electromagnetic field in a medium whose dispersion and nonlinear properties can be described by the cubic-quintic Duffing model, i.e., by an oscillator with third-and fifth-order anharmonicity. A system of equations governing the evolution of a unidirectional electromagnetic wave is analyzed without using the approximation of slowly varying envelopes. Three types of solutions of this system describing stationary propagation of a pulse in such a medium are found. When the signs of the anharmonicity constants are different, then the amplitude of a steady-state pulse is limited, but its energy may grow on account of an increase in its duration. The characteristics of such a pulse, referred to as an electromagnetic domain, are discussed.