ar X iv : m at h - ph / 0 40 10 40 v 1 2 2 Ja n 20 04 FACTORIZATIONS OF ODE ’ S WITH POLYNOMIAL NONLINEARITIES ∗
نویسنده
چکیده
We propose a factorization scheme for ordinary differential equations with polynomial nonlinearities (reaction-diffusion in the traveling frame and dampedanharmonic-oscillator equations) which is different and more efficient than that given by L.M. Berkovich in Sov. Math. Dokl. 45, 162 (1992). We then invert the factorization brackets in the SUSYQM style to get ODE’s with a different polynomial nonlinearity but displaying kink solutions of different width propagating at the same velocity as the kink solution of the original equation. We thus report an interesting pairing of this class of differential equations from the standpoint of their kink solutions that could have applications still unforeseen. We illustrate the mathematical procedure with several important cases, among which the generalized Fisher equation and the FitzHugh-Nagumo equation.
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