Abstract
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In this article, our aim is to further extend the applications of modified extended direct algebraic method on new coupled systems, which have many important applications in mathematical physics. many exact solutions out of which some are new in different forms such as soliton, solitary wave, periodic, elliptic function solutions of new coupled KdV and new coupled Zakharov-Kuznetsov (ZK) systems are constructed by employing this method. The constructed exact solutions are also presented graphically. The modulation instability is utilized to discuss the stability of obtained solutions. All solutions are stable and exact solutions. The obtained results show that the modified extended method is general and effective. Furthermore, many other new coupled systems arising in mathematical physics can also be solved by this powerful and effective method.