Abstract
We study the propagation of M-shaped solitons and kink-periodic waves in an optical fiber medium exhibiting Kerr dispersion and quintic nonlinearity by applying the symbolic computation with ansatz functions technique and logarithmic transformation. We used seven different methods, namely, three waves technique, homoclinic breather technique, M-shaped solitons, single exponential form, double exponential form, kink cross-rational and trigonometric and hyperbolic ansatz approaches. The quintic derivative nonlinear Schrodinger equation (QD-NLSE) is applied to model for ultrashort light pulse in fibers and self-steepening processes. We compute two categories of M-shaped solitons and their dynamics are revealed in figures by appropriate values of parameters. Moreover two types of interaction of M-shaped solitons with kink wave are revealed. We attain multiwaves, kink cross-rational (KCR), Homoclinic breather, periodic cross-rational solutions (PCRs) for governing model. Finally, the stability property of all solutions is analytically studied under the finite selection of parameters.