On solving the (3+1)-dimensional NLEQZK equation and the (3+1)-dimensional NLmZK equation using the extended simplest equation method

Abstract

The extended simplest equation method is employed in this article to construct many solitons and other solutions for two nonlinear partial differential equations (PDEs), namely the (3+1)-dimensional nonlinear extended quantum Zakharov–Kuznetsov (NLEQZK) equation and the (3+1)-dimensional nonlinear modified Zakharov–Kuznetsov (NLmZK) equation which play an important role in mathematical physics. The first equation is performed in quantum electron–positron–ion magnetoplasmas, while the second equation governs the behavior of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in the presence of a uniform magnetic field. Comparison of our new results obtained in this article for the two considered models with the other well-known results is also provided.