Perturbation of plane waves for the fourth-order defocusing Schrödinger equation

Abstract By performing a perturbation analysis on the plane wave solutions of the fourth-order defocusing nonlinear Schrödinger (FODNLS) equation, this study successfully derived the classical Korteweg–de Vries (KdV) equation and the fifth-order KdV equation. The results show that the soliton solutions of the KdV hierarchy can directly describe the energy density of small-amplitude FODNLS solitons and indirectly determine their phase characteristics. Further theoretical analysis reveals that different higher-order dispersion terms within the KdV hierarchy correspond to higher-order corrections to the group velocity of FODNLS solitons. To validate these conclusions, we used the asymptotic solutions of the KdV solitons to generate various initial conditions and systematically studied the dynamics of FODNLS solitons through numerical simulations.