| Summary: | In this article we have discussed the analytical analysis of two dimensional modified Korteweg–de Vries (mK–dV) equation arising in plasma physics that governs the ion-acoustic solitary waves for their asymptotic behavior because of the trapping of electrons using auxiliary equation mapping method. By using this technique we have obtained some quite general and new variety of exact traveling wave solutions which are collecting some kind of semi half bright, bright, dark, semi half dark, doubly periodic, combined, periodic, half hark and half bright via three parametric values which is the primary key point of difference of our technique. These results are highly applicable to develop new theories of quantum mechanics, biomedical problems, soliton dynamics, plasma physics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, biomedical problems, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions via Mathematica 10.4 to get more understanding of different new dynamical shapes of solutions.
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