别洛乌索夫-扎伯廷斯基方程（Belousov-Zhabotinsky equation)是一组模拟化学反应扩散的非线性偏微分方程：

u_{t}=du_{xx}+u(1-r*u-u)

v_{t}=v_{xx}-suv

解析解
:u(x, t) = 1/(4(1+r))-(1/2)coth(_C1-(1/12)\sqrt(6)x/\sqrt(d)-(5/12)t)/(1+r)+(1/4)coth(_C1-(1/12)\sqrt(6)x/sqrt(d)-(5/12)*t)^2/(1+r)
:u(x, t) = 1/(4(1+r))-(1/2)tanh(_C1-(1/12)\sqrt(6)x/\sqrt(d)-(5/12)t)/(1+r)+(1/4)tanh(_C1-(1/12)\sqrt(6)x/sqrt(d)-(5/12)*t)^2/(1+r)
:u(x, t) = 1/(4(1+r))-(1/2I)cot(_C1-(1/2)x/\sqrt(-6d)-(5/12I)t)/(1+r)-(1/4)cot(_C1-(1/2)x/\sqrt(-6d)-(5/12I)t)^2/(1+r)
:u(x, t) = 1/(4(1+r))-(1/2I)tan(_C1-(1/2)x/\sqrt(-6d)+(5/12I)t)/(1+r)-(1/4)tan(_C1-(1/2)x/\sqrt(-6d)+(5/12I)t)^2/(1+r)
:u(x, t) = 1/(4(1+r))-(1/2I)tan(_C1+(1/2)x/\sqrt(-6d)+(5/12I)t)/(1+r)-(1/4)tan(_C1+(1/2)x/\sqrt(-6d)+(5/12I)t)^2/(1+r)

行波图
参考文献

*谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社

*阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年

李志斌编著 《非线性数学物理方程的行波解》 科学出版社

#王东明著 《消去法及其应用》 科学出版社 2002

*何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445

#Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press

Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997

#Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
#Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
#Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
#Dongming Wang, Elimination Practice,Imperial College Press 2004

David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004

George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759