The exact soliton wave solutions of the nonlinear evolution equation with variable coefficients

In this article, we investigated new traveling wave solutions of the modified Zakharov–Kuznetsov equation with an additional time-dependent variable coefficient using the functional variable method. The proposed method is reliable and effective, and it yields more general exact solutions compared with several existing techniques. The obtained exact solutions are of significant importance for revealing the internal mechanisms of the underlying physical phenomena, and the graphical illustrations help to better understand their physical characteristics. It is shown that the proposed method provides a powerful mathematical tool for solving other nonlinear wave equations arising in mathematical physics and engineering.

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