KdV-Burgers也称Burgers-KdV方程是一个非线性偏微分方程：

u_{t}+uu_{x}-\alphau_{xx}-\beta*u_{xxx}=0

解析解
:u(x, t) = (1/25)(-3+250\beta^2_C3)/\beta+(6/25)coth(_C1-(1/10)x/\beta+_C3t)/\beta+(3/25)coth(_C1-(1/10)x/\beta+_C3*t)^2/\beta
:u(x, t) = (1/25)(-3+250\beta^2_C3)/\beta+(6/25)tanh(_C1-(1/10)x/\beta+_C3t)/\beta+(3/25)tanh(_C1-(1/10)x/\beta+_C3*t)^2/\beta
:u(x, t) = -(1/25)(3+250\beta^2_C3)/\beta-(6/25)tanh(_C1+(1/10)x/\beta+_C3t)/\beta+(3/25)tanh(_C1+(1/10)x/\beta+_C3*t)^2/\beta
:u(x, t) = (1/25)(-(250I)\beta^2_C3-3)/\beta-(6/25I)tan(_C1-(1/10I)x/\beta+_C3t)/\beta-(3/25)tan(_C1-(1/10I)x/\beta+_C3*t)^2/\beta
:u(x, t) = (1/25)(-(250I)\beta^2_C3-3)/\beta+(6/25I)cot(_C1-(1/10I)x/\beta+_C3t)/\beta-(3/25)cot(_C1-(1/10I)x/\beta+_C3*t)^2/\beta

行波图
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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