Stability analysis and solutions of (2+1)-Kadomtsev-Petviashvili equation by homoclinic technique based on Hirota bilinear form - Yokus, Asif; Isah, Muhammad Abubakar (Springer, 2022)
The Kadomtsev-Petviashvili equation used in this article is used to model shallow water waves with weakly nonlinear restorative forces as well as waves in a strong magnetic medium. The bilinear form of the equation is constructed and several new exact solutions are discovered using the ansatz as an exponential function and the new homoclinic approach based on the Hirota bilinear form. The exact solutions as seen in the three-dimensional graphs indicate the evolution of periodic properties. In this article, the modulation instability is applied to study stability of the solutions. For this evolution equation, the findings revealed new mechanical structures as well as new properties. In this article, 3D, density graphs and some physical dynamics of traveling wave solutions produced by the newly proposed homoclinic approach to strengthen the Hirota bilinear method are analyzed. All of the discovered solutions are put into the equation to ensure their existence. The connection between the wave's phase velocity and the number of waves is discussed by means of traveling wave solutions that allow the discussion of the phenomenon of dispersion of a wave. Also, taking into account the newly discovered traveling wave solutions for the Kadomtsev-Petviashvili equation, the propagation of the traveling wave in the direction of x and y is studied. These findings provide us a fresh doorway for us to examine the model in deep. The existing work is widely used to report a variety of fascinating physical occurrences in the domains of shallow water waves, ferromagnetic mediums, and other similar phenomena.
Keywords: Kadomtsev-Petviashvili equation; Hirota bilinear method; Homoclinic approach; Periodic-waves solution; Traveling wave solution