变形KdV-Burgers(Modified KdV-Burgers equation)是一个非线性偏微分方程：

u_{t}+u_{xxx}-\alphau^2u_{x}-\beta*u_{xx}=0

解析解
:u(x, t) = -(1/6)\beta\sqrt(6)/\sqrt(\alpha)-\sqrt(6)_C2cot(_C1+_C2x+(-2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = -(1/6)\beta\sqrt(6)/\sqrt(\alpha)-\sqrt(6)_C2coth(_C1+_C2x+(2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = -(1/6)\beta\sqrt(6)/\sqrt(\alpha)+\sqrt(6)_C2tan(_C1+_C2x+(-2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = -(1/6)\beta\sqrt(6)/\sqrt(\alpha)-\sqrt(6)_C2tanh(_C1+_C2x+(2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = (1/6)\beta\sqrt(6)/\sqrt(\alpha)+\sqrt(6)_C2cot(_C1+_C2x+(-2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = (1/6)\beta\sqrt(6)/\sqrt(\alpha)+\sqrt(6)_C2coth(_C1+_C2x+(2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = (1/6)\beta\sqrt(6)/\sqrt(\alpha)-\sqrt(6)_C2tan(_C1+_C2x+(-2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)
:u(x, t) = (1/6)\beta\sqrt(6)/\sqrt(\alpha)+\sqrt(6)_C2tanh(_C1+_C2x+(2_C2^3+(1/6)\beta^2_C2)*t)/\sqrt(\alpha)

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