五阶KdV方程 解析解
解析失败 (转换错误。服务器（“https://wikimedia.org/api/rest_”）报告：“Cannot get mml. upstream request timeout”): {\displaystyle u(x,t)=_{C}5-(3*(-4*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\beta ^{2}*_{C}5^{2}-8*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\gamma ^{2}*_{C}5^{2}-(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\beta *_{C}5^{3}*\alpha -(3/2)*\gamma *(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{3}*\alpha +(1/4)*\gamma *(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{3}*\beta ^{2}/\delta +(2/5)*\gamma ^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{3}*\beta /\delta -\beta ^{2}*_{C}5^{4}*\alpha +4800*_{C}3^{6}*\beta *\delta ^{2}*_{C}5-160*_{C}3^{4}*\beta ^{2}*_{C}5^{2}*\delta -800*\delta ^{2}*\alpha *_{C}3^{4}*_{C}5^{2}+16*\gamma ^{2}*_{C}5^{3}*\beta *_{C}3^{2}-320*\gamma ^{2}*_{C}3^{4}*_{C}5^{2}*\delta +7200*\gamma *_{C}3^{6}*\delta ^{2}*_{C}5+10*\gamma *\beta ^{2}*_{C}5^{3}*_{C}3^{2}-3*\gamma *_{C}5^{4}*\beta *\alpha -48000*_{C}3^{8}*\delta ^{3}+2*\beta ^{3}*_{C}5^{3}*_{C}3^{2}+8*\gamma ^{3}*_{C}5^{3}*_{C}3^{2}-2*\gamma ^{2}*_{C}5^{4}*\alpha +10*_{C}5^{4}*\delta *\alpha ^{2}+20*\gamma *_{C}5^{3}*\delta *\alpha *_{C}3^{2}-480*\gamma *_{C}3^{4}*_{C}5^{2}*\beta *\delta -12*\gamma *_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}*\beta +40*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\alpha *_{C}5^{2}+120*_{C}3^{4}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\gamma *_{C}5+120*_{C}3^{4}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\beta *_{C}5-1200*_{C}3^{6}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta ^{2}+40*_{C}5^{3}*\delta *\alpha *\beta *_{C}3^{2}+(1/20)*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\beta ^{3}*_{C}5^{3}/\delta +(1/5)*\gamma ^{3}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{3}/\delta ))*JacobiSN(_{C}2+_{C}3*x+(1/25)*_{C}3*(3*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5*\beta *\gamma +45*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *_{C}5*\alpha +(1/2*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2})))*\alpha *_{C}5^{2}*\beta -150*_{C}3^{4}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\beta -9*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\gamma ^{2}*_{C}5-(9/4*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2})))*\gamma *\alpha *_{C}5^{2}+90*_{C}3^{4}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\gamma +(1/20)*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}*\beta *\gamma ^{2}/\delta -(1/20)*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}*\beta ^{2}*\gamma /\delta +(3/10)*\gamma ^{3}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}/\delta +420*_{C}3^{4}*\delta *_{C}5*\beta *\gamma +3600*_{C}3^{6}*\delta ^{2}*\gamma +300*_{C}3^{4}*\delta *_{C}5*\beta ^{2}-6000*_{C}3^{6}*\delta ^{2}*\beta +2*_{C}5^{2}*\beta *\gamma ^{2}*_{C}3^{2}-2*_{C}5^{2}*\beta ^{2}*\gamma *_{C}3^{2}+_{C}5^{3}*\beta *\gamma *\alpha -130*_{C}5^{2}*\delta *\alpha *\beta *_{C}3^{2}+15*_{C}5^{3}*\delta *\alpha ^{2}+12*\gamma ^{3}*_{C}5^{2}*_{C}3^{2}-3*\gamma ^{2}*_{C}5^{3}*\alpha -360*_{C}3^{4}*\gamma ^{2}*\delta *_{C}5)*t/(\delta *(-\alpha *_{C}5+2*\gamma *_{C}3^{2}+(1/20)*\gamma *(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))/\delta )),(1/20)*{\sqrt {(}}10)*{\sqrt {(}}(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))/\delta )/_{C}3)^{2}/(60*_{C}3^{4}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\beta -6*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\gamma ^{2}*_{C}5+60*_{C}3^{4}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *\gamma -3*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5*\beta ^{2}-(3/2*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2})))*\gamma *\alpha *_{C}5^{2}-(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\alpha *_{C}5^{2}*\beta +(1/20)*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\beta ^{3}*_{C}5^{2}/\delta -120*_{C}3^{4}*\delta *_{C}5*\beta ^{2}+10*_{C}5^{2}*\beta ^{2}*\gamma *_{C}3^{2}+16*_{C}5^{2}*\beta *\gamma ^{2}*_{C}3^{2}-240*_{C}3^{4}*\gamma ^{2}*\delta *_{C}5-3*_{C}5^{3}*\beta *\gamma *\alpha -\beta ^{2}*_{C}5^{3}*\alpha +2400*_{C}3^{6}*\delta ^{2}*\beta +2400*_{C}3^{6}*\delta ^{2}*\gamma +10*_{C}5^{3}*\delta *\alpha ^{2}+8*\gamma ^{3}*_{C}5^{2}*_{C}3^{2}-2*\gamma ^{2}*_{C}5^{3}*\alpha +2*\beta ^{3}*_{C}5^{2}*_{C}3^{2}-360*_{C}3^{4}*\delta *_{C}5*\beta *\gamma +20*_{C}5^{2}*\delta *\alpha *\beta *_{C}3^{2}+(2/5)*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}*\beta *\gamma ^{2}/\delta +(1/4)*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}*\beta ^{2}*\gamma /\delta -9*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5*\beta *\gamma +30*_{C}3^{2}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*\delta *_{C}5*\alpha +(1/5)*\gamma ^{3}*(2*\gamma *_{C}5+_{C}5*\beta -40*\delta *_{C}3^{2}+{\sqrt {(}}4*\gamma ^{2}*_{C}5^{2}+4*\gamma *_{C}5^{2}*\beta +_{C}5^{2}*\beta ^{2}-40*\delta *\alpha *_{C}5^{2}))*_{C}5^{2}/\delta )}