We study the propagation of few-cycle optical solitary waves in a nonlinear media under the combined action of quadratic, cubic and quintic nonlinearities in a large phase-mismatched second harmonic (SHG) process. Exact bright and dark soliton solutions to the nonlinear evolution equation for cascaded quadratic media beyond the slowly varying envelope approximations is reported. The analytical solutions obtained are verified through numerical simulations.Keywords: nonlinear Schrödinger equation, ultrashort,cascaded nonlinearity, few-cycle, soliton (Some figures may appear in colour only in the online journal) Considerable research effort is made in the investigation of few optical pulses owing to the recent progress in the generation of few-cycle and even sub-cycle optical pulses [1][2][3][4][5][6]. Such ultrashort optical pulses have possible applications in many diverse areas such as, high-order harmonic generation, ultrafast spectroscopy, metrology, medical diagnostics and imaging, testing of high-speed devices, optical communications, manipulation of chemical reactions and bond formation, material processing, investigations of light-matter interactions and attosecond physics [1,2]. In this context, it is clear that study of few-cycle pulse propagation phenomena in various media is of tremendous importance. Till recently, most of the pulse propagation models were derived to describe many-cycle pulses using the so called slowly varying envelope approximation (SVEA) [7]. However, it is now well established that the description of few-cycle pulses requires a modification of the SVEA. Many propagation models have been proposed and successfully studied to a varying degree [1-2,4]. Most of these models are aimed at describing few-cycle pulses in cubic nonlinear media [8][9][10][11][12][13]. However, recently the analysis of ultrashort optical pulse propagation in second-order nonlinear material is getting tremendous boost, particularly media with cascaded-quadratic nonlinearity is drawing particular attention [14][15][16][17][18][19][20][21]. In 2006, Moses and Wise have derived a coupled propagation equations for ultrashort pulses in a degenerate three-wave mixing process in quadratic ( 2 ) media [14]. Moses-Wise model is restricted to the case of strongly mismatched interaction where the conversion efficiency to second or higher harmonics is negligible. In fact, a more generalized nonlinear envelope equation is derived by Conforti et al. to describe the propagation of broadband optical pulses in second order nonlinear materials [15,16]. However, Moses and Wise went on to present, using cascaded quadratic nonlinearity, theoretical and experimental evidence of a new quadratic effect, namely the controllable self-steepening (SS) effect. The controllability of the SS effect is very useful in nonlinear propagation of ultrashort pulses as it may be used to cancel the propagation effects of group velocity mismatch. It is pointed out that the cascaded nonlinearity induces a Raman-like term into the model owing to t...