New Optical Soliton Structures, Bifurcation Properties, Chaotic Phenomena, and Sensitivity Analysis of Two Nonlinear Partial Differential Equations

In this work, we provide new optical soliton structures of the Kadomtsev-Petviashvili equation in (3 + 1)-dimensional and the Jimbo-Miwa equation in (3 + 1)-dimensional together with some intriguing new analysis, chaotic phenomena, bifurcation properties, and sensitivity analysis. Since soliton structure with three analyses is a very interesting recent topic in nonlinear dynamics, we extract different chaotic structures, bifurcation analysis together with phase portrait and sensitivity of our mentioned nonlinear partial differential equations. Applications of the Kadomtsev-Petviashvili equation are in sonic waves, magneto sonic waves, superfluid, weakly nonlinear quasi-unidirectional waves, shallow water waves with weakly nonlinear restoring forces and frequency dispersion, plasma physics, etc. Advanced intellect could benefit from studying the Jimbo-Miwa equation, which addresses specific fascinating higher-dimensional waves in marine engineering, ocean sciences, various interesting physical structures in the areas of optics, acoustic, mathematical modeling, epidemics, circuit analysis, computational neuroscience, intergalactic modeling, etc. Due to the huge applications of the mentioned equations, there is a high demand to investigate with recently developed three analyses. Making use of the recently developed advanced strategy, the adaptive, compatible, further advanced closed-form solitary wave structures are harvested to the mentioned equations in the present manuscript. All these scientifically accomplished exact soliton structures, which take the forms of rational functions and trigonometric functions could assist in our comprehension of remarkable nonlinear challenging situations. In contrast to the present outcomes, our newly formed discoveries will exhibit unique features. The outcomes that were extracted confirm that the recommended technique is meticulously planned, intuitive, and advantageous for measuring the dynamic behavior of nonlinear evolution equations within contemporary science and technology.