Stability Analysis Solutions for the Fourth-Order Nonlinear Ablowitz-Kaup-Newell-Segur Water Wave Equation

Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy appears naturally in the model besides a string equation. The Korteweg-de Vries hierarchy is contained in the AKNS hierarchy as a reduction, and therefore appears in the model before one takes the double scaling limit. The AKNS hierarchy is a complexified version of the