| Abstract: |
| The nonclassical symmetries method is a powerful extension of the classical method for finding exact solutions of differential equations. The challenge with the method, however, is that the governing equations for admitted nonclassical symmetries of a given equation are typically coupled and nonlinear and therefore dificult to solve. Fortunately, nonclassical symmetries of a given equation may be derived (at least for simple equations) from corresponding nonclassical symmetries of a simpler equation via an equivalent transformation. We construct, as an illustration of this routine, nontrivial nonclassical symmetries of the Black-Scholes equation. We exploit an equivalence transformation between the Black-Scholes equation and the heat equation to construct the nonclassical symmetries of the Black-Scholes equation. We further illustrate, courtesy of the results by Arrigo, Goard, and Broadbridge in J. Math. Anal. Appl. 202 (1996), 259-279, that the resulting new reduction solutions of the Black-Scholes equation are in fact classical reduction solutions. |
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