Computational simulation for the (1 + 1)-dimensional Ito equation arising quantum mechanics and nonlinear optics

Abstract

This research paper investigates the numerical solutions of the (1 + 1)-dimensional Ito equation through the extended simplest equation (ESE) method. This model is considered as well-known in quantum mechanics and nonlinear optics, which represents the height of the water's free surface above a flat bottom. The obtained solitary solutions emerge the localized wave packet as a persistent and dominant feature. Diverse novel computational solutions are constructed and demonstrated through three distinct types of sketches. The stability of our obtained solutions is investigated by using Hamiltonian system's characterizations. The novelty of our paper is explained by comparing our obtained solutions with the previously evaluated computational solutions with different computational schemes.