广田-萨摩方程(Hirota Satsuma equation)是一个三元非线性偏微分方程组：
:\begin{cases} u_t-\frac{1}{2}u_{xxx}+3uu_x-3(vw)_x=0,\\
v_t+v_{xxx}-3uv_x=0,\\
w_t+w_{xxx}-3uw_x=0.\end{cases}

解析解
:u(x, t) = -(1/3)(-_C3+_C2^3)/_C2, v(x, t) = 0, w(x, t) = _C7+_C8cos(_C1+_C2x+_C3t)
:u(x, t) = -(1/3)(-_C3+_C2^3)/_C2, v(x, t) = 0, w(x, t) = _C7+_C8sin(_C1+_C2x+_C3t)
:u(x, t) = (1/3)(_C3+_C2^3)/_C2, v(x, t) = 0, w(x, t) = _C7+_C8cosh(_C1+_C2x+_C3t)
:u(x, t) = (1/3)(_C3+_C2^3)/_C2, v(x, t) = 0, w(x, t) = _C7+_C8sinh(_C1+_C2x+_C3t)
:u(x, t) = -(1/3)(9_C3^3-_C4)/_C3, v(x, t) = _C6-(3/4)_C9cos(_C2+_C3x+_C4t)+_C9cos(_C2+_C3x+_C4*t)^3, w(x, t) = 0
:u(x, t) = -_C2^2+2_C2^2coth(_C1+_C2x-_C2^3t)^2, v(x, t) = _C5+_C6coth(_C1+_C2x-_C2^3*t), w(x, t) = 0
:{u(x, t) = -(1/2)_C2^2+2_C2^2csc(_C1+_C2x-(1/2)_C2^3t)^2, v(x, t) = _C5+_C6csc(_C1+_C2x-(1/2)_C2^3t), w(x, t) = 0}
:{u(x, t) = (1/2)_C2^2+2_C2^2csch(_C1+_C2x+(1/2)_C2^3t)^2, v(x, t) = _C5+_C6csch(_C1+_C2x+(1/2)_C2^3t), w(x, t) = 0}
:u(x, t) = -(1/3)(-_C4-2_C3^3+_C3^3_C1^2)/_C3-2_C3^2JacobiDN(_C2+_C3x+_C4t, _C1)^2, v(x, t) = (2/3)_C3(2_C4-2_C3^3+_C3^3_C1^2)_C8/_C9^2-(2/3)_C3(2_C4-2_C3^3+_C3^3_C1^2)JacobiDN(_C2+_C3x+_C4t, _C1)/_C9, w(x, t) = _C8+_C9JacobiDN(_C2+_C3x+_C4t, _C1)
:u(x, t) = -(1/3)(-_C4+_C3^3_C1^2+_C3^3)/_C3+2_C3^2_C1^2JacobiSN(_C2+_C3x+_C4t, _C1)^2, v(x, t) = -(2/3)_C1^2_C3(_C3^3_C1^2+_C3^3+2_C4)_C10/_C11^2+(2/3)_C3_C1^2(_C3^3_C1^2+_C3^3+2_C4)JacobiSN(_C2+_C3x+_C4t, _C1)/_C11, w(x, t) = _C10+_C11JacobiSN(_C2+_C3x+_C4t, _C1)
:u(x, t) = (1/3)(-2_C3^3+4_C3^3_C1^2-_C4)/_C3+(2_C3^2-2_C3^2_C1^2)JacobiNC(_C2+_C3x+_C4t, _C1)^2, v(x, t) = _C6, w(x, t) = _C10
:u(x, t) = -(1/2)_C3^2+_C3^2_C1^2-2_C3^2_C1^2JacobiCN(_C2+_C3x+(-(1/2)_C3^3+_C3^3_C1^2)t, _C1)^2, v(x, t) = _C6+_C7JacobiCN(_C2+_C3x+(-(1/2)_C3^3+_C3^3_C1^2)t, _C1), w(x, t) = 0
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行波图
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