Unveiling solitons and traveling wave solutions with modulation instability analysis for extended (3+1)-dimensional seventh-order standard Ito and modified Ito equations

Abstract

In this study, the extended (3+1)-dimensional seventh-order standard Ito and modified Ito equations are investigated. The study applied, for the first time, the modified Sardar sub-equation technique (MSSET) to the extended standard Ito equation and the extended modified Ito equation. Various types of solutions are achieved by MSSET for both types of the Ito equations. Among the obtained solutions are the bright, dark and singular soliton solutions as well as hyperbolic solutions, exponential solutions, rational solutions and singular periodic solutions. The MSSET, with robustness, direct calculations and low computational cost properties, succeeded to provide a variety of solution forms. In this work, novel solutions for extended seventh-order modified Ito equation are achieved that were not available in the literature before. Also, this work investigated the extended seventh-order standard Ito equation for the first time and provided novel solutions for it. The achieved solutions in this work were verified by direct substitution into the investigated Ito equations and proved to satisfy them. Also, the novelty of this work was the derivation of modulation instability analysis for the equations under study using linear stability analysis for the first time in the literature. For graphical representation, two-dimensional, three-dimensional graphics and contour plots of some achieved analytic solutions, for both of the investigated Ito equations, were provided with suitable values of parameters satisfying the limiting conditions.