Stability analysis, modulation instability, and the analytical wave solitons to the fractional Boussinesq-Burgers system

The research is concerned with the novel analytical solitons to the ( 1 + 1 )-D nonlinear Boussinesq-Burgers System ( B-B S) in the sense of a new definition of fractional derivatives. The concerned system is helpful to describes the waves in different phenomenons, including proliferation of waves in shallow water, oceanic waves and many others. Authors gain the solutions involving trigonometric, hyperbolic, and rational functions by using the expo function and the extended sinh-Gordon equation expansion ( EShGEE ) methods. Fractional derivative provides the better results than the present results. These results are helpful and useful in the different areas of applied sciences, including the optical fi bers, telecommunications, plasma physics, fl uid dynamics and many more. The solutions are shown by 2-dimensional, 3-dimensional, and contour graphs. The solutions are useful in further studies of the governing model. The stability process is performed to verify that the solutions are exact and accurate. The modulation instability is used to determine the steady-state stable results to the governing equation. The techniques utilized are both simple and effective.