Lump wave, breather wave and other abundant wave solutions to the (2 + 1)-dimensional Sawada–Kotera–Kadomtsev Petviashvili equation of fluid mechanics

Abstract

The (2 + 1)-dimensional Sawada–Kotera–Kadomtsev Petviashvili equation (SKKPe) is explored in this work. Wielding the Hopf–Cole transform, its Hirota bilinear form is developed. Then, the lump wave solutions of the bright-type and dark-type, and the breather wave solutions of the sin–cosh type are extracted by applying the Hirota bilinear method with symbolic computation by taking different test functions. Additionally, abundant travelling wave solutions like the bright wave, periodic wave and singular wave solutions are investigated by employing three effective approaches, namely the extend Wang’s direct mapping method II (EWDMM), Bernoulli sub-equation function method (BSEFM) and Kudryashov method (KM). The nonlinear physical characteristics of the attained solutions are displayed graphically using the 3D and 2D plots. To the best of the author's knowledge, the results presented in the article are entirely new and have not been presented elsewhere, which can augment the exact solutions of the considered equation and allow us to study its nonlinear dynamics better.