查看“︁加德纳-KP方程”︁的源代码


'''加德纳-KP方程'''（Gardner-KP equation）是一个非线性[[偏微分方程]]<ref>Shafiof and Sousaraei,New Solutions for Positive and Negaive Gardner-KP Equation, World Applied Sciences Journal 13(4) 622-666,2011</ref>

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

==行波解==

加德纳-KP方程有行波解：

<math>{u(x, y, t) = -1/2-_C2*sech(_C1+_C2*x+_C3*y-(1/2)*(-3*_C2^2+2*_C3^2+2*_C2^4)*t/_C2)}</math>
<math>{u(x, y, t) = -1/2-_C3*JacobiDN(_C2+_C3*x+_C4*y+(1/2)*(3*_C3^2-2*_C4^2+2*_C3^4*_C1^2-4*_C3^4)*t/_C3, _C1)}</math>
<math>{u(x, y, t) = -1/2+_C3*JacobiDN(_C2+_C3*x+_C4*y+(1/2)*(3*_C3^2-2*_C4^2+2*_C3^4*_C1^2-4*_C3^4)*t/_C3, _C1)}</math>
<math>{u(x, y, t) = -1/2-I*_C2*coth(_C1+_C2*x+_C3*y+(1/2)*(3*_C2^2-2*_C3^2+4*_C2^4)*t/_C2)}</math>
<math>{u(x, y, t) = -1/2-I*_C2*csc(_C1+_C2*x+_C3*y+(1/2)*(3*_C2^2-2*_C3^2+2*_C2^4)*t/_C2)}</math>
<math>{u(x, y, t) = -1/2-I*_C2*tan(_C1+_C2*x+_C3*y-(1/2)*(-3*_C2^2+2*_C3^2+4*_C2^4)*t/_C2)}</math>
<math>{u(x, y, t) = -1/2-I*_C3*JacobiND(_C2+_C3*x+_C4*y+(1/2)*(3*_C3^2-2*_C4^2)*t/_C3, sqrt(2))}</math>
<math>{u(x, y, t) = -1/2-(1/2*I)*\sqrt(2)*_C3*JacobiNC(_C2+_C3*x+_C4*y+(1/2)*(3*_C3^2-2*_C4^2)*t/_C3, (1/2)*\sqrt(2))}</math>

==图集==
<gallery>
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


</gallery>

==参考文献==
<references/>

[[Category:非线性偏微分方程]]