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In this article, we apply the two variable G′G,1G-expansion method with the aid of symbolic computation to construct many new exact solutions for two higher-order nonlinear partial differential equatuions (PDEs) namely, the higher-order nonlinear Schrö dinger (NLS) equation with derivative non-kerr nonlinear terms describing pulse of the propagation beyond ultrashort range in optical communication systems and the higher-order nonlinear quantum Zakharov-Kuznetsov (QZK) equation which arises in quantum magneto plasma. Also, based on Liénard equation, we find many other diffrent new soliton solutions of the above NLS equation. Soliton solutions, periodic solutions, rational functions solutions and Jacobi elliptic functions solutions are obtained. Comparing our new solutions obtained in this article with the well-known solutions are given. [ABSTRACT FROM AUTHOR]