這篇文章中，我們探討離散型反應擴散方程u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t))，其中
反應項f(u)=u^2(1-u)。在此，
我們證明此方程式存在一種全解其動態行為宛如兩個來自x軸兩端相向而行的行波。

This paper deals with a discrete reaction-diffusion equation
u_t(x,t)=u(x+1,t)-2u(x,t)+u(x-1,t)+f(u(x,t)),
where f(u)=u^2(1-u). Here, we prove there exist entire solutions which behave as two
traveling waves coming from both sides of x-axis.

[1] X. Chen and J.-S. Guo, Existence and asymptotic stability of traveling waves
of discrete quasilinear monostable equations, Journal of Differential Equations
184 (2002), 549-569.
[2] X. Chen and J.-S. Guo, Uniqueness and existence of traveling waves for discrete
quasilinear monostable dynamics, Mathematische Annalen 326 (2003), 123-146.
[3] X. Chen, S.-C. Fu and J.-S. Guo, Uniqueness and asymptotics of traveling waves
of monostable dynamics on lattices, SIAM Journal on Mathematical Analysis
38 (2006), 233-258.
[4] R.A Fisher, The advance of adavantageous genes, Annals Eugenics 7 (1937),
355-369.
[5] J.-S. Guo and Y. Morita, Entire solutions of reaction-diffusion equations and an
application to discrete diffusive equations, Discrete and Continuous Dynamical
Systems 12 (2005), 193-212.
[6] A. Kolmogorov, I. Petrovsky, and N. Piskunov, Etude de l’´equation de la diffusion
avec croissance de la quantit´e de mati´ere et son application ´a un probl´eme
biologique, Bulletin Universite d’Etat a Moscow Series Internationale Section
A 1 (1937), 1-26.