耦合KdV方程组(Coupled KdV equation)是一个二元非线性偏微分方程组：

u_{t}+6\alphauu_{x}-6vv_{x}+\alphau_{xxx}=0

v_{t}+3\alphauv_{x}+\alphav_{xxx}=0

解析解
:u(x, t) = (1/3)(-_C3+\alpha_C2^3)/(\alpha_C2)-2_C2^2csc(_C1+_C2x+_C3t)^2, v(x, t) = -(1/3)\sqrt(12\alpha_C2^4+6_C2_C3)csc(_C1+_C2x+_C3*t)
:u(x, t) = (1/3)(-_C3+\alpha_C2^3)/(\alpha_C2)-2_C2^2sec(_C1+_C2x+_C3t)^2, v(x, t) = -(1/3)\sqrt(12\alpha_C2^4+6_C2_C3)sec(_C1+_C2x+_C3*t)
:u(x, t) = (1/3)(-_C3+2\alpha_C2^3)/(\alpha_C2)-2_C2^2coth(_C1+_C2x+_C3t)^2, v(x, t) = -(1/3)\sqrt(6_C2_C3+24\alpha_C2^4)coth(_C1+_C2x+_C3t)
:u(x, t) = (1/3)(-_C3+2\alpha_C2^3)/(alpha_C2)-2_C2^2tanh(_C1+_C2x+_C3t)^2, v(x, t) = -(1/3)\sqrt(6_C2_C3+24alpha_C2^4)tanh(_C1+_C2x+_C3t)
:u(x, t) = -(1/3)(_C3+\alpha_C2^3)/(\alpha_C2)-2_C2^2csch(_C1+_C2x+_C3t)^2, v(x, t) = -(1/3)\sqrt(6_C2_C3-12alpha_C2^4)csch(_C1+_C2x+_C3*t)
:u(x, t) = -(1/3)(_C3+8\alpha_C2^3)/(\alpha_C2)-4_C2^2tan(_C1+_C2x+_C3t)^2, v(x, t) = -(1/6)(_C3+8\alpha_C2^3)\sqrt(2)/(_C2\sqrt(\alpha))-2\sqrt(2)\sqrt(\alpha)_C2^2tan(_C1+_C2x+_C3*t)^2
:u(x, t) = (1/3)(-_C4+\alpha_C3^3+\alpha_C3^3_C1^2)/(\alpha_C3)-2_C3^2JacobiNS(_C2+_C3x+_C4t, _C1)^2, v(x, t) = -(1/3)\sqrt(12\alpha_C3^4_C1^2+12\alpha_C3^4+6_C3_C4)JacobiNS(_C2+_C3x+_C4t, _C1)
:u(x, t) = (1/3)(-_C4+\alpha_C3^3+\alpha_C3^3_C1^2)/(\alpha_C3)-2_C3^2_C1^2JacobiSN(_C2+_C3x+_C4t, _C1)^2, v(x, t) = -(1/3)\sqrt(12\alpha_C3^4_C1^2+12\alpha_C3^4+6_C3_C4)_C1JacobiSN(_C2+_C3x+_C4t, _C1)
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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

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李志斌编著 《非线性数学物理方程的行波解》 科学出版社

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