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In this work, we probe the Gardner equation and the modified Benjamin-Bona-Mahony (mBBM) equation associated with plasma physics, acoustic-gravity waves in fluid mechanics, hydro-magnetic waves in cold plasma etc Exact wave solutions to the mentioned equations are studied analytically by the enhanced modified simple equation (EMSE) method. The solitary wave solutions are determined including free parameters. Setting definite values of the unknown parameters yield useful and stable solitary wave solutions. We have depicted some 3D and 2D graphs of the obtained solutions to comprehend the physical structure of the tangible events.

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