Abstract
In this manuscript, the Lie point symmetries, conservation laws, and traveling wave reductions have all been derived. Also, new forms of soliton solutions of generalized q-deformed equation via means of unified method has been extracted. Implementing this approach the results of governing model are obtained as rational and polynomial functions. The unified technique is used to analyze solitary solutions, soliton solutions, also periodic rational solutions. Additionally, to illustrate the various solitons’ propagation characteristics, several illustrations are used to display their statistical data. The bifurcation is introduced on the governing equation. The planer system has been extracted. Taking all possible cases for the parameters, the behavior has been shown by portraits in phase plane. The proposed equation has expanded modeling possibilities for complex processes with broken symmetry.
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