The distortion study of rogue waves of the generalized nonlinear Schrodinger equation under the third-order dispersion perturbation

We have investigated the robustness of the rogue wave solutions of two reductions of the generalized nonlinear Schrodinger equation with the third-order dispersion perturbation term. The two reductions are the nonlinear Schrodinger (NLS) equation and the second-type derivative nonlinear Schrodinger (DNLSII) equation. The perturbed equations have practical physical application value. However, they are non-integrable so their exact rogue wave solutions can hardly be obtained by analytical methods. In this paper, we use numerical methods to simulate the perturbed rogue wave solutions and use the quantitative analysis method to assess the robustness of the rogue wave solutions. Two criteria c and r are defined based on the definition of rogue waves in ocean science to analyze the distortion degree of rogue waves quantitatively. The numerical simulation results and the values of these criteria show that the rogue wave solutions of these two reductions are robust under the third-order dispersion perturbation, while the rogue wave solution of the DNLSII equation is more sensitive to the perturbation than that of the NLS equation.