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In this paper, the evolutionary Cahn–Allen equation is upgraded into the generalized two-mode version via Korsunsky’s sense. The new established model is characterized in terms of the wave propagation form represented by the movement of two simultaneous waves of symmetric type. The Kudryashov-expansion method is used to extract some solitary wave solutions to the suggested model. Moreover, from mathematical point of view, some physical properties are explored to the two-mode Cahn–Allen equation via examining, graphically, the effect of the phase velocity and the dispersion parameters acting on the propagations of the obtained bidirectional wave-solutions. Finally, very interesting types of solutions are obtained to the new model by implementing a modified versions of the rational sine–cosine and sinh–cosh methods.