色散长波方程组 ((2+1)D dispersive long wave equation)是一个二元非线性偏微分方程组：.
u_{xt}+v_{xx}+0.5*(u^2)_{xy}=0
v_{t}+(u*v+u_{xy})_{x}=0
解析解
: {u(x, y, t) = -1._C5/_C3-2._C3sec(_C2+_C3x+_C4y+_C5t), v(x, t) = _C4_C3-2._C4_C3sec(_C2+_C3x+_C4y+_C5*t)^2}
: {u(x, y, t) = -1._C5/_C3+2._C3sec(_C2+_C3x+_C4y+_C5t), v(x, t) = _C4_C3-2._C4_C3sec(_C2+_C3x+_C4y+_C5*t)^2}
: {u(x, y, t) = -1._C5/_C3-1.414_C3JacobiNC(_C2+_C3x+_C4y+_C5t, .707), v(x, t) = -1._C4_C3JacobiNC(_C2+_C3x+_C4y+_C5t, .707)^2}
: {u(x, y, t) = -1._C5/_C3-1.414_C3JacobiNC(_C2+_C3x+_C4y+_C5t, .707), v(x, t) = -1._C4_C3JacobiNC(_C2+_C3x+_C4y+_C5t, .70710678118654752440)^2}
: {u(x, y, t) = -1._C5/_C3-2._C3JacobiND(_C2+_C3x+_C4y+_C5t, 1.414), v(x, t) = -2._C4_C3JacobiND(_C2+_C3x+_C4y+_C5t, 1.414)^2}
: {u(x, y, t) = -1._C5/_C3-2.\sqrt(-1.+_C1^2)_C3JacobiND(_C2+_C3x+_C4y+_C5t, _C1), v(x, t) = -2._C4_C3+_C4_C3_C1^2+(2._C4_C3-2._C4_C3_C1^2)JacobiND(_C2+_C3x+_C4y+_C5t, _C1)^2}
: {u(x, y, t) = -1._C5/_C3-2.\sqrt(-1.+_C1^2)_C3JacobiND(_C2+_C3x+_C4y+_C5t, _C1), v(x, t) = -2._C4_C3+_C4_C3_C1^2+(2._C4_C3-2._C4_C3_C1^2)JacobiND(_C2+_C3x+_C4y+_C5t, _C1)^2}
: {u(x, y, t) = -1._C5/_C3+2.\sqrt(-1._C1^2+1.)_C3JacobiNC(_C2+_C3x+_C4y+_C5t, _C1), v(x, t) = -2._C4_C3_C1^2+_C4_C3+(-2._C4_C3+2._C4_C3_C1^2)JacobiNC(_C2+_C3x+_C4y+_C5*t, _C1)^2}
行波图
参考文献
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