Solitons and other solutions for higher-order NLS equation and quantum ZK equation using the extended simplest equation method

Abstract In this article, we apply the extended simplest equation method for constructing the solitons and other solutions of two nonlinear partial differential equations (PDEs), namely the higher-order nonlinear Schrodinger (NLS) equation with derivative non-Kerr nonlinear terms and the nonlinear quantum Zakharov–Kuznetsov (QZK) equation which play an important role in mathematical physics. The first equation describes pulse of the propagation beyond ultrashort range in optical communication systems, while the second equation arises in quantum magneto plasma. Comparison of our new results in this article with the well-known results is given.

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