We analytically solved the higher-order nonlinear Schrödinger (HNLS) equation with non-Kerr nonlinearity under some parametric conditions and investigated explicitly bright and dark solitary wave solutions. Periodic wave solutions are also presented. The functional form of the bright and dark solitons presented are different from fundamental known sech(.) and tanh(.) respectively. We have estimated theoretically the size of the derivative non-Kerr nonlinear coefficients of the HNLS equation that agreed the reality of the waveguide made of highly nonlinear optical materials, could be used as the model parameters for sub-10fs pulse propagation.PACS numbers: 42.81. Dp, 05.45.Yv, 42.65.Tg, 42.79.Sz Optical solitons have promising potential to become principal information carriers in telecommunication due to their capability of propagating long distance without attenuation and changing their shapes. Considerable attentions are being paid theoretically and experimentally to analyze the dynamics of optical solitons in optical waveguide. The waveguides used in the picosecond optical pulse propagation in nonlinear optical communication systems are usually of Kerr type and consequently the dynamics of light pulses are described by nonlinear Schrödinger (NLS) family of equations with cubic nonlinear terms [1]. The validity of the NLS equation as a reliable model is dependent on the assumption that the spacial width of the soliton is much larger than the carrier wavelength. This is equivalent to the condition that the width of the soliton frequency spectrum is much less than the carrier frequency. The robustness of the optical soliton makes it useful for long distance optical communication systems, the high frequency of the optical carrier makes possible a high bit rate, and to increase the bit rate further it is desirable to use shorter femtosecond pulses and in order to model the propagation of a femtosecond (<100fs) optical pulse in an optical fiber, higher order nonlinear Schrödinger equation (HNLS) (not including optical fiber loss) [2]Here z is the normalized distance along the fiber, t is the normalized time with the frame of the reference moving along the fiber at the group velocity. The subscripts z and t denotes the spatial and temporal partial derivatives respectively. The coefficients a i (i = 1, 2, ..., 5), particularly, (a 1 = β2 2 , a 2 = γ 1 , a 3 = β3 6 , a 4 = − γ1 ω0 and a 5 = γ 1 T R ) are the real parameters related to group velocity dispersion (GVD), self phase * Electronic address: amitava˙ch26@yahoo.com(A. Choudhuri) modulation (SPM), third-order dispersion (TOD), self steepening and self-frequency shift due to stimulated Raman scattering (SRS) respectively. Here β j = (is the dispersion coefficients evaluated at the carrier frequency ω 0 , with β 1 , the inverse of group velocity, β 2 , the group velocity dispersion parameter, β 3 third order dispersion (TOD) parameter and so on. β is propagation constant. More specifically, γ 1 is coefficient of cubic nonlinearity, which results from the intensi...
