Higher order solitons in non-paraxial optics

In last two decades actively are studied the phenomena resulting from the evolution of ultrashort optical pulses in nonlinear dispersive media. The well-known (1+1D) nonlinear Schrödinger equation (NSE) describes very well the propagation of narrow-band optical pulses (Δω<<ω0). Nowadays, it is quite easy to obtain broad-band phase-modulated femtosecond laser pulses or to reach the attosecond region where Δω≈ω0. To explore their behavior it is necessary to use the more general nonlinear amplitude equation (NAE). In local time coordinate system it differs from the standard NSE with two additional non-paraxial terms. In present paper, by using the NAE, it is investigated the dynamics of higher order non-paraxial solitons. It is shown that the peak of soliton is linearly shifted in time domain. This temporal shift is observed in the frames of non-paraxial optics, even when the higher order nonlinear and dispersive effects are neglected.