Abstract
In this paper , we study the problem of constructing the new solutions of the mKdV equation and STO equation. By using the Airy equation and its solution, the new solutions of mKdV equation and STO equation are constructed. First of all, through function transformation, mKdV equation and STO equation can be turned into Airy function to solve. Then, construct the solution of mKdV equation and STO equation by using the solution of Airy function. Finally, analyze the properties of these solutions with the help of symbolic computation system: Mathematica.
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