An Exactly Solvable Travelling Wave Equation in the Fisher–KPP Class
An Exactly Solvable Travelling Wave Equation in the Fisher–KPP Class
复制标题
Fisher-KPP 类中可精确解的行波方程
DOI：
10.1007/s10955-015-1350-6
复制
发表时间：
2015
影响因子：
1.6
通讯作者：
B. Derrida
中科院分区：
文献类型：
--
作者：
E. Brunet;B. Derrida
对于一个简单的一维格点形式的行波方程，我们得到了初始条件和波前在任意以后时刻的位置之间的精确关系。这个精确的关系采取了一个反问题的形式：给定行波到达位置n的时间t_n，可以推导出初始轮廓。我们表明，通过复杂的分析，一些已知的性质的行波方程的Fisher-KPP类可以恢复，特别是Bramson的位移的位置。我们还恢复和推广Ebert-van Saarloos的修正依赖于初始条件。
For a simple one dimensional lattice version of a travelling wave equation, we obtain an exact relation between the initial condition and the position of the front at any later time. This exact relation takes the form of an inverse problem: given the times $$t_n$$tn at which the travelling wave reaches the positions n, one can deduce the initial profile. We show, by means of complex analysis, that a number of known properties of travelling wave equations in the Fisher–KPP class can be recovered, in particular Bramson’s shifts of the positions. We also recover and generalize Ebert–van Saarloos’ corrections depending on the initial condition.