Abstract
In this paper, the solitary solutions of the (1 + 1)-dimensional Benjamin–Bona–Mahony and strain wave equations are set up by employing the simplest equation method for the first time. By determining the value of parameters, the images of the traveling wave solutions are displayed, and they intuitively reflect that choosing different Bernoulli equations will affect the form of solutions. The validity and wider applicability of the method for solving known wave phenomena models are verified, moreover, the solution structure is enriched.
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