In this work, we study the effect of fundamental and higher order soliton with and without the presence of third-order dispersion (TOD, β3). The effect is studied near the zero dispersion wavelength of 1270 nm with second-order dispersion (β2) value of 0.22 ps2/km for various third-order dispersion parameter sweeps from 0.01 to 0.1 ps3/km. The theme of temporal pulse displacement due to TOD is studied for 10 and 20 soliton periods for fundamental soliton and 10 soliton period for higher order soliton (N = 2). The effective pulse width of 1 ps (FWHM) is displaced from its original position to adjacent position depending upon the TOD value. It is found in both fundamental and higher order soliton, that the displacement in higher for TOD value of 0.1 ps3/km than 0.01 ps3/km. The effect of displaced fundamental soliton pulse is pictured with respect to the transmitted distance (different soliton period) and TOD. The spectral characteristics of higher order soliton is also analyzed which is one of the characteristic mechanisms for supercontinuum generation. © 2014 World Scientific Publishing Company.