非规范变形KdV方程 (Unnormalized modified KdV equation)是一个非线性偏微分方程：

u_{t}+u_{xxx}+\alphau^2u_{x}=0

解析解
: {u(x, t) = \sqrt(6)_C2sech(_C1+_C2x-_C2^3t)/\sqrt(\alpha)}
: u(x, t) = \sqrt(6)_C3JacobiDN(_C2+_C3x+(-2_C3^3+_C3^3_C1^2)t, _C1)/\sqrt(\alpha)
: u(x, t) = \sqrt(-6\alpha(-1+_C1^2))_C3JacobiND(_C2+_C3x+(-2_C3^3+_C3^3_C1^2)t, _C1)/\alpha
: u(x, t) = \sqrt(6)_C1_C3JacobiCN(-_C2-_C3x-(-2_C3^3_C1^2+_C3^3)*t, _C1)/\sqrt(\alpha)
: {u(x, t) = \sqrt(6)\sqrt(\alpha(-1+_C1^2))_C3JacobiNC(-_C2-_C3x-(-2_C3^3_C1^2+_C3^3)t, _C1)/\alpha}
: u(x, t) = -6_C3JacobiNS(_C2+_C3x+(_C3^3_C1^2+_C3^3)t, _C1)/\sqrt(-6\alpha)
: u(x, t) = -\sqrt(6)_C3JacobiDN(_C2+_C3x+(-2_C3^3+_C3^3_C1^2)t, _C1)/\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