加德纳-KP方程（Gardner-KP equation）是一个非线性偏微分方程[1]
(ut+6uux+6u2*ux+uxxx)x+uyy=0
加德纳-KP方程有行波解：
u(x,y,t)=−1/2−C2*sech(C1+C2*x+C3*y−(1/2)*(−3*C22+2*C32+2*C24)*t/C2) u(x,y,t)=−1/2−C3*JacobiDN(C2+C3*x+C4*y+(1/2)*(3*C32−2*C42+2*C34*C12−4*C34)*t/C3,C1) u(x,y,t)=−1/2+C3*JacobiDN(C2+C3*x+C4*y+(1/2)*(3*C32−2*C42+2*C34*C12−4*C34)*t/C3,C1) u(x,y,t)=−1/2−I*C2*coth(C1+C2*x+C3*y+(1/2)*(3*C22−2*C32+4*C24)*t/C2) u(x,y,t)=−1/2−I*C2*csc(C1+C2*x+C3*y+(1/2)*(3*C22−2*C32+2*C24)*t/C2) u(x,y,t)=−1/2−I*C2*tan(C1+C2*x+C3*y−(1/2)*(−3*C22+2*C32+4*C24)*t/C2) u(x,y,t)=−1/2−I*C3*JacobiND(C2+C3*x+C4*y+(1/2)*(3*C32−2*C42)*t/C3,sqrt(2)) u(x,y,t)=−1/2−(1/2*I)*(2)*C3*JacobiNC(C2+C3*x+C4*y+(1/2)*(3*C32−2*C42)*t/C3,(1/2)*(2))
