前沿选择不由重正化群稳定性决定
Front Selection Is Not Determined by Renormalization-Group Stability
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中文总结 AI 辅助
该研究以FKPP方程为对象，借助RG框架证明其行波解构成连续RG不动点族，v≥2的前沿均RG稳定，但渐近选择的前沿不由RG稳定性决定，明确二者为不同概念。
中文摘要 AI 辅助
费希尔-柯尔莫哥洛夫-彼得罗夫斯基-皮斯库诺夫（Fisher--Kolmogorov--Petrovsky--Piskunov，FKPP）方程是前沿传播与渐近态选择的典型范例。我们采用统一的重正化群（RG）框架，证明其行波解构成连续的RG不动点族，且所有速度v≥2的前沿均为RG稳定；但渐近选择的前沿不由RG稳定性决定，因此FKPP方程提供了RG不动点稳定性与渐近态选择为不同概念的明确例证。
英文摘要
The Fisher--Kolmogorov--Petrovsky--Piskunov equation provides a paradigmatic example of front propagation and asymptotic-state selection. Using a unified renormalization-group (RG) framework, we show that its traveling-wave solutions form a continuous family of RG fixed points and that all fronts with $v \ge 2$ are RG-stable. Nevertheless, the asymptotically selected front is not determined by RG stability. The FKPP equation therefore provides an explicit example in which RG fixed-point stability and asymptotic-state selection are distinct concepts.
