這篇論文主要是對於行進波在等溫化學反應 A + nB ->(n+1)B (其中A是反應物，B是自動催化劑)的發展作一個概括性的介紹。存在一個最小波速使得行進波解存在的充分必要條件為其波速大於或等於此一最小波速。我們將討論早期研究對於此最小波速的估計。

[1]
D. G. Aronson and H. F. Weinberger,Multidimensional diffusion arising in population genetics,Adv. Math. 30(1978)
,33-76.

[2]
N. J. T. Bailey, The mathematical theory of infectious diseases, Griffen,London,(1975).

[3]
J. Billingam and D.J. Needham, The development of traveling
wave in quadratic and cubic autocatalysis with unequal diffusion rates. I. Permanent form traveling waves, Phil.
Trans. Roc. Soc. A 334 (1991), 1-24.

[4]
J. Billingam and D. J. Needham, The development of traveling wave in quadratic and cubic autocatalysis with
unequal diffusion rates. II. An initial value problem with
immobilized or nearly immobilized autocatalyst, Phil. Trans. Roc. Soc. A 336 (1991), 497-539.

[5]
X. Chen and J.-S. Guo, Existence and asymptotic stability
of traveling waves of discrete quasilinear monostable equations, J. Differential Equations 184 (2) (2002),
549-569.

[6]
X. Chen and Y. W. Qi, Sharp estimates on minimum traveling
wave speed of reaction diffusion systems modelling autocatalysis, SIAM J. Math. Anal. 39 (2007), no. 2, 437-448.

[7]
P. C. Fife and J. B. McLeod, The approach of nonlinear diffusion equations to traveling wave front solutions, Arch. Ration. Mech. Anal. 65 (1977), 335-361.

[8]
Y. Hosono, Phase plane analysis of traveling waves for higher order autocatalytic reaction-diffusion systems,
Discrete Contin. Dyn. Syst. Ser. B, 8 (2007), 115-125.

[9]
Y. Hosono, Propagation speeds of traveling fronts for higher order autocatalytic reaction-diffusion systems,
Japan J. Indust. Appl. Math. 24, (2007), 79-104. 12

[10]
J. H. Merkin and D. J. Needham, Propagating reaction-diffusion waves in a simple isothermal quadratic autocatalytic chemical systems, J. Eng. Math. 23 (1989)
, 343-356.

[11]
J. H. Merkin and D. J. Needham, The development of traveling waves in a simple isothermal chemical II. Cubic
autocatalysis with quadratic and linear decay, Proc. Roy.
Soc. London A, 430 (1990), 315-345.

[12]
J. H. Merkin and D. J. Needham, The development of traveling waves in a simple isothermal chemical IV. Cubic
autocatalysis with quadratic and linear decay, Proc. Roy.
Soc. London A, 434 (1991), 531-554.

[13]
Y.W.Qi,The development of traveling waves in cubic auto-catalysis with different rates of diffusion, Physica D
226 (2007), 129-135.
[14]
D. Sattinger, On the stability of waves of nonlinear parabolic systems, Adv. Math. 22 (1976), 312-355.

[15]
H. Takase and B. D. Sleeman, Traveling wave solutions
to monostable reaction-diffusion systems of mixed monotone
type, Proc. Roy. Soc. Lond. A, 455 (1999), 1561-1598.

[16]
J. Xin, Front propagation in heterogeneous media, SIAM Rev.
42 (2000), 161-230. 13