加德纳-KP方程

加德纳-KP方程（Gardner-KP equation）是一个非线性偏微分方程

(u_t+6uu_x+6u^2*u_x+u_xxx)_x+u_yy=0

行波解
加德纳-KP方程有行波解：

{u(x, y, t) = -1/2-_C2sech(_C1+_C2x+_C3y-(1/2)(-3_C2^2+2_C3^2+2_C2^4)t/_C2)}
{u(x, y, t) = -1/2-_C3JacobiDN(_C2+_C3x+_C4y+(1/2)(3_C3^2-2_C4^2+2_C3^4_C1^2-4_C3^4)t/_C3, _C1)}
{u(x, y, t) = -1/2+_C3JacobiDN(_C2+_C3x+_C4y+(1/2)(3_C3^2-2_C4^2+2_C3^4_C1^2-4_C3^4)t/_C3, _C1)}
{u(x, y, t) = -1/2-I_C2coth(_C1+_C2x+_C3y+(1/2)(3_C2^2-2_C3^2+4_C2^4)*t/_C2)}
{u(x, y, t) = -1/2-I_C2csc(_C1+_C2x+_C3y+(1/2)(3_C2^2-2_C3^2+2_C2^4)*t/_C2)}
{u(x, y, t) = -1/2-I_C2tan(_C1+_C2x+_C3y-(1/2)(-3_C2^2+2_C3^2+4_C2^4)*t/_C2)}
{u(x, y, t) = -1/2-I_C3JacobiND(_C2+_C3x+_C4y+(1/2)(3_C3^2-2_C4^2)t/_C3, sqrt(2))}
{u(x, y, t) = -1/2-(1/2I)\sqrt(2)_C3JacobiNC(_C2+_C3x+_C4y+(1/2)(3_C3^2-2_C4^2)t/_C3, (1/2)*\sqrt(2))}

图集
File:Gardner-KP 6.gif
File:Gardner-KP 5.gif
File:Gardner-KP 4.gif
File:Gardner-KP 3.gif
File:Gardner-KP 2.gif

参考文献