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This research explores bifurcation of a nonlinear model concerning with the telecommunication strait. Possible all phase plane diagrams due to various parametric conditions are found. Derivation of analytical tangled wave propagating solutions following all phase orbits of the corresponding phase portraits are established. As a results, the soliton, shock wave, singular soliton, periodic wave and singular periodic solutions are obtained by direct integration from Hamiltonian energy function. The periodic solutions of the model are formulated in the form of generalized Jacobi elliptic functions, which also provide the solitonic solution setting the value of beta is unity. Additionally, chaotic and quasi-periodic behaviors have been found for a range of parameter values after adding the perturbed term. The perturbed system's quasi-periodic and chaotic behavior have been demonstrated using sensitivity analysis. Finally, picturesque explorations are delivered exposing effects of exist parameters of the gained wave solutions. The majority of the achieved results are derived for the first time. Moreover, the solutions show that the novel schemes are very simple, outright, fruitful and successful and that they can be used in wide range of other nonlinear partial differential equations (NLPDEs), which create different kinds of dynamical features of other wave model. • Analyze bifurcations of the nonlinear telecommunication model. • Found various phase portraits with distinct parametric conditions of the model. • Derive solitons, Jacobi elliptic wave solutions following each phase orbits. • Demonstrate quasi-periodic, chaotic behaviors using sensitivity analysis. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider a (3+1)-dimensional Sharma-Tasso-Olver-like (STOL) model, which can be used to describe dispersive wave phenomena in optics, plasmas, quantum physics, and others. Based on the simplified Hirota approach, the n-soliton solutions are obtained. We observe that the collisions are non-elastic fusion or fission phenomena where some kink waves disappear due to soliton fusion, or a single kink wave splits into more kink waves due to soliton fusion. We derive kinky-lump breather, combo line kink and kinky-lump breather, and a pair of kinky-lump breather wave solutions that degenerate from two-, three- and four-solitons respectively by choosing complex conjugate values involving free parameters. Moreover, we demonstrate a few new collisions of the Jacobi elliptic sine function with one soliton, and a periodic cosine function which provides kinky-periodic waves and double-periodic waves. All special properties of those collision solutions are illustrated with the 3D, density and contour plots. • We consider (3+1)-dimensional Sharma-Tasso-Olver-like model. • The solitons, periodic, Jacobi elliptic functions and its interactions are obtained. • We observed the interactions as non-elastic fusion or fission phenomena. • The solutions are illustrated with the 3D, density and contour plots. [ABSTRACT FROM AUTHOR]