mKdV方程是一个非线性偏微分方程：

u_{t}+6u^2u_{x}+u_{xxx}=0

解析解
:u(x, t) = \sqrt(6)_C2sech(_C1+_C2x-_C2^3t)
:u(x, t) = \sqrt(6)_C3JacobiDN(_C2+_C3x+(-2_C3^3+_C3^3_C1^2)t, _C1)
:u(x, t) = \sqrt(-6+6_C1^2)_C3JacobiNC(-_C2-_C3x-(_C3^3-2_C3^3_C1^2)*t, _C1)
:u(x, t) = \sqrt(6-6_C1^2)_C3JacobiND(_C2+_C3x+(-2_C3^3+_C3^3_C1^2)*t, _C1)
:u(x, t) = \sqrt(6)_C1_C3JacobiCN(-_C2-_C3x-(_C3^3-2_C3^3_C1^2)*t, _C1)
:u(x, t) = -I\sqrt(6)_C2cot(_C1+_C2x-2_C2^3t)
:u(x, t) = -I\sqrt(6)_C2coth(_C1+_C2x+2_C2^3t)
:u(x, t) = -I\sqrt(6)_C2csc(_C1+_C2x+_C2^3*t)
:u(x, t) = -I\sqrt(6)_C2tanh(_C1+_C2x+2_C2^3t)
:u(x, t) = -I\sqrt(6)_C2sec(_C1+_C2x+_C2^3*t)
:u(x, t) = -I\sqrt(6)_C2csch(_C1+_C2x-_C2^3*t)
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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

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

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#Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
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