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))
