Dynamics characteristics of soliton structures of the new (3 + 1) dimensional integrable wave equations with stability analysis

Abstract

This study investigates optical solitons solutions within the framework of the two new (3 + 1)-dimensional integrable wave equations by employing the modified Sardar sub-equation method. The importance of these suggested models span diverse fields including geophysics, seismology, medical imaging, photonics and sensor development. The derived solutions, meticulously verified using Mathematica, encompass a rich array of mathematical functions including trigonometric, hyperbolic, and exponential functions. Visualization techniques, such as 3D plots, 2D plots, density graphs, contour graphs and polar graphs, effectively illustrate the diverse behaviors exhibited by these soliton solutions. These behaviors include lump, periodic, kink, dark, bright, peakons, cuspons, compactons soliton waves and other complex phenomena. Moreover the modulation instability of the consider model is examined, and corresponding conditions are established. The soliton solutions highlight the efficiency and effectiveness of these method in discovering traveling wave solutions, presenting a valuable tool for addressing a range of nonlinear evolution equations arising in diverse scientific fields such as hydrodynamics, optical fiber communications, plasma physics, ocean engineering, nonlinear dynamics, and condensed matter physics.