关于Fisher-KPP方程的有限种群变体
On a Finite Population Variation of the Fisher-KPP Equation
AI总结：
本研究构建了Fisher-KPP方程的有限种群变体，证明其存在行波闭式解，还构造了有限区间平衡问题的闭式近似并数值分析了两个相关猜想。
摘要：
本文利用反应项可通过两人两策略斜对称博弈的复制动态生成这一事实，构建了Fisher-KPP方程的有限种群变体。我们借助Ablowitz和Zeppetella的已有研究结果，证明所得偏微分方程组存在行波解，且该行波有闭式解。值得注意的是，该闭式解由经典Fisher方程已知闭式解的符号反转构造而来。我们还针对带Dirichlet和Neumann边界条件的有限区间上的对应平衡问题，构造了闭式解近似。文中提出了关于这些对应平衡问题的两个猜想，并进行了数值分析。
英文摘要：
In this paper, we formulate a finite population variation of the Fisher-KPP equation using the fact that the reaction term can be generated from the replicator dynamic using a two-player two-strategy skew-symmetric game. We use prior results from Ablowitz and Zeppetella to show that the resulting system of partial differential equations admits a travelling wave solution, and that there are closed form solutions for this travelling wave. Interestingly, the closed form solution is constructed from a sign-reversal of the known closed form solution of the classic Fisher equation. We also construct a closed form solution approximation for the corresponding equilibrium problem on a finite interval with Dirichlet and Neumann boundary conditions. Two conjectures on these corresponding equilibrium problems are presented and analysed numerically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
