多项式非线性项下扭结的超对称配对
Supersymmetric pairing of kinks for polynomial nonlinearities
摘要：
我们展示了如何可以获得扭结解的多项式非线性常微分方程的一个有效的因式分解过程直接相关的非线性多项式部分的因式分解。我们主要讨论了反应扩散方程的运动标架和阻尼非谐振子方程。我们还报告了一个有趣的配对的扭结的解决方案，通过扭转超对称量子力学风格的因子分解括号得到的结果。这样，得到了具有不同多项式非线性项的常微分方程，它们具有不同宽度的扭结解，但以与原方程的扭结相同的速度传播。这对扭结可以有许多应用。我们用几个重要的例子来说明数学过程，其中包括广义Fisher方程，FitzHugh-Nagumo方程和微管聚合前沿
英文摘要：
We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on reaction-diffusion equations in the travelling frame and damped-anharmonic-oscillator equations. We also report an interesting pairing of the kink solutions, a result obtained by reversing the factorization brackets in the supersymmetric quantum mechanical style. In this way, one gets ordinary differential equations with a different polynomial nonlinearity possessing kink solutions of different width but propagating at the same velocity as the kinks of the original equation. This pairing of kinks could have many applications. We illustrate the mathematical procedure with several important cases, among which the generalized Fisher equation, the FitzHugh-Nagumo equation, and the polymerization fronts of microtubules
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