Rogue Wave And Qualitative Analysis Of The Higher-order Dispersive Nonlinear Schr(?)dinger Equation

In recent years, studies on rogue waves have been very popular in the optical fibersand the ocean science.This dissertation focuses on the solutions and properties of rogue waves of thehigher-order dispersive nonlinear Schr dinger (HDNLS) equation. Firstly, we explainthe process of modified Darboux transformation (mDT) and point out the significantdifference between the mDT and the traditional Darboux transformation (DT).Secondly, we use the method of mDT and undetermined coefficients to get the first-and second-order rational solutions of the HDNLS equation, the pictures of which arerogue waves. There are two free parameters both in the fist-order and second-orderrational solutions. The procedure which use the property of symmetric is also bepresented in this dissertation. Based on above results, we plot the figures of theserational solutions and the contour maps of them by taking specific free parameters.With the help of these contour figures and the numerical method, we find out themaximum and minimum points of every rational solution. At the same time, we alsoanalyze the influence of little perturbation with the help of graphical simulation.Finally, we explore the coordinate transformation between the rational solutions of theHDNLS equation and the nonlinear Schr dinger (NLS) equation. Based on thecalculation, it can be obtained that this transformation does not exist. The rationalsolutions of the HDNLS equation change into rational solutions of the NLS equationwhen the little perturbation equals0. Additionally, the Fourier transforms of theserational solutions have been gotten, this study may be useful to predict the appearanceof rogue waves.