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 Schrodinger equation (NSE) describes very well the propagation of narrow-band optical pulses (Delta omega<<omega(0)). Nowadays, it is quite easy to obtain broad-band phase-modulated femtosecond laser pulses or to reach the attosecond region where Delta omega approximate to omega(0). 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.