五阶KdV方程

五阶KdV方程(Fifth order KdV equation)是一个非线性偏微分方程，简称fKdV方程： $u_t+\alpha \ast u^2\ast u_x+\beta \ast u_x\ast u_{xx}+\gamma \ast u\ast u_{xxx}+\delta \ast u_{xxxxx}=0$

解析解

$u(x,t)=6{\ast }_C{3}^2\ast (-(6\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast {\gamma }^2/\alpha +(60\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast \delta -72\ast \delta \ast {\gamma }^2+720\ast {\delta }^2\ast \alpha -120\ast \delta \ast {\beta }^2)\ast JacobiND{(}_{C}2{+}_{C}3\ast x-(6\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2))){\ast }_C{3}^5\ast t/\alpha ,\sqrt{(}2){)}^2/(\beta \ast (6\ast {\beta }^2-120\ast \delta \ast \alpha +12\ast {\gamma }^2+12\ast \beta \ast \gamma +6\ast \sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))$

$u(x,t)=6{\ast }_C{3}^2\ast (-(6\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast {\gamma }^2/\alpha +(60\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast \delta -72\ast \delta \ast {\gamma }^2+720\ast {\delta }^2\ast \alpha -120\ast \delta \ast {\beta }^2)\ast JacobiNS{(}_{C}2{+}_{C}3\ast x-(6\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2))){\ast }_C{3}^5\ast t/\alpha ,I{)}^2/(\beta \ast (6\ast {\beta }^2-120\ast \delta \ast \alpha +12\ast {\gamma }^2+12\ast \beta \ast \gamma +6\ast \sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))$

$u(x,t)=-3{\ast }_C{3}^2\ast (-(3/2)\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2))\ast {\gamma }^2/\alpha +(15\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast \delta -18\ast \delta \ast {\gamma }^2+180\ast {\delta }^2\ast \alpha -30\ast \delta \ast {\beta }^2)\ast JacobiCN{(}_{C}2{+}_{C}3\ast x-(3/2)\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma -\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)){\ast }_C{3}^5\ast t/\alpha ,(1/2)\ast \sqrt{(}2){)}^2/(\beta \ast ((3/2)\ast {\beta }^2-30\ast \delta \ast \alpha +3\ast {\gamma }^2+3\ast \beta \ast \gamma +(3/2)\ast \sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))$

$u(x,t)=-6{\ast }_C{3}^2\ast (-(6\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma +\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast {\gamma }^2/\alpha +(60\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma +\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))\ast \delta -72\ast \delta \ast {\gamma }^2+720\ast {\delta }^2\ast \alpha -120\ast \delta \ast {\beta }^2)\ast JacobiDN{(}_{C}2{+}_{C}3\ast x-(6\ast (-12\ast \delta \ast \alpha +{\beta }^2+2\ast \beta \ast \gamma +\sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2))){\ast }_C{3}^5\ast t/\alpha ,\sqrt{(}2){)}^2/(\beta \ast (6\ast {\beta }^2-120\ast \delta \ast \alpha +12\ast {\gamma }^2+12\ast \beta \ast \gamma -6\ast \sqrt{(}-40\ast \delta \ast \alpha \ast {\beta }^2+{\beta }^4+4\ast {\beta }^3\ast \gamma +4\ast {\beta }^2\ast {\gamma }^2)))$

$u(x,t){=}_{C}5-(3\ast (-4{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\beta }^2{\ast }_C{5}^2-8{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\gamma }^2{\ast }_C{5}^2-(2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \beta {\ast }_C{5}^3\ast \alpha -(3/2)\ast \gamma \ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^3\ast \alpha +(1/4)\ast \gamma \ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^3\ast {\beta }^2/\delta +(2/5)\ast {\gamma }^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^3\ast \beta /\delta -{\beta }^2{\ast }_C{5}^4\ast \alpha +4800{\ast }_C{3}^6\ast \beta \ast {\delta }^2{\ast }_{C}5-160{\ast }_C{3}^4\ast {\beta }^2{\ast }_C{5}^2\ast \delta -800\ast {\delta }^2\ast \alpha {\ast }_C{3}^4{\ast }_C{5}^2+16\ast {\gamma }^2{\ast }_C{5}^3\ast \beta {\ast }_C{3}^2-320\ast {\gamma }^2{\ast }_C{3}^4{\ast }_C{5}^2\ast \delta +7200\ast \gamma {\ast }_C{3}^6\ast {\delta }^2{\ast }_{C}5+10\ast \gamma \ast {\beta }^2{\ast }_C{5}^3{\ast }_C{3}^2-3\ast \gamma {\ast }_C{5}^4\ast \beta \ast \alpha -48000{\ast }_C{3}^8\ast {\delta }^3+2\ast {\beta }^3{\ast }_C{5}^3{\ast }_C{3}^2+8\ast {\gamma }^3{\ast }_C{5}^3{\ast }_C{3}^2-2\ast {\gamma }^2{\ast }_C{5}^4\ast \alpha +10{\ast }_C{5}^4\ast \delta \ast {\alpha }^2+20\ast \gamma {\ast }_C{5}^3\ast \delta \ast \alpha {\ast }_C{3}^2-480\ast \gamma {\ast }_C{3}^4{\ast }_C{5}^2\ast \beta \ast \delta -12\ast \gamma {\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2\ast \beta +40{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \alpha {\ast }_C{5}^2+120{\ast }_C{3}^4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \gamma {\ast }_{C}5+120{\ast }_C{3}^4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \beta {\ast }_{C}5-1200{\ast }_C{3}^6\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\delta }^2+40{\ast }_C{5}^3\ast \delta \ast \alpha \ast \beta {\ast }_C{3}^2+(1/20)\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\beta }^3{\ast }_C{5}^3/\delta +(1/5)\ast {\gamma }^3\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^3/\delta ))\ast JacobiSN{(}_{C}2{+}_{C}3\ast x+(1/25){\ast }_{C}3\ast (3{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_{C}5\ast \beta \ast \gamma +45{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta {\ast }_{C}5\ast \alpha +(1/2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)))\ast \alpha {\ast }_C{5}^2\ast \beta -150{\ast }_C{3}^4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \beta -9{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\gamma }^2{\ast }_{C}5-(9/4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)))\ast \gamma \ast \alpha {\ast }_C{5}^2+90{\ast }_C{3}^4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \gamma +(1/20)\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2\ast \beta \ast {\gamma }^2/\delta -(1/20)\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2\ast {\beta }^2\ast \gamma /\delta +(3/10)\ast {\gamma }^3\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2/\delta +420{\ast }_C{3}^4\ast \delta {\ast }_{C}5\ast \beta \ast \gamma +3600{\ast }_C{3}^6\ast {\delta }^2\ast \gamma +300{\ast }_C{3}^4\ast \delta {\ast }_{C}5\ast {\beta }^2-6000{\ast }_C{3}^6\ast {\delta }^2\ast \beta +2{\ast }_C{5}^2\ast \beta \ast {\gamma }^2{\ast }_C{3}^2-2{\ast }_C{5}^2\ast {\beta }^2\ast \gamma {\ast }_C{3}^2{+}_C{5}^3\ast \beta \ast \gamma \ast \alpha -130{\ast }_C{5}^2\ast \delta \ast \alpha \ast \beta {\ast }_C{3}^2+15{\ast }_C{5}^3\ast \delta \ast {\alpha }^2+12\ast {\gamma }^3{\ast }_C{5}^2{\ast }_C{3}^2-3\ast {\gamma }^2{\ast }_C{5}^3\ast \alpha -360{\ast }_C{3}^4\ast {\gamma }^2\ast \delta {\ast }_{C}5)\ast t/(\delta \ast (-\alpha {\ast }_{C}5+2\ast \gamma {\ast }_C{3}^2+(1/20)\ast \gamma \ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))/\delta )),(1/20)\ast \sqrt{(}10)\ast \sqrt{(}(2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))/\delta ){/}_{C}3{)}^2/(60{\ast }_C{3}^4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \beta -6{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\gamma }^2{\ast }_{C}5+60{\ast }_C{3}^4\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta \ast \gamma -3{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_{C}5\ast {\beta }^2-(3/2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)))\ast \gamma \ast \alpha {\ast }_C{5}^2-(2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \alpha {\ast }_C{5}^2\ast \beta +(1/20)\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast {\beta }^3{\ast }_C{5}^2/\delta -120{\ast }_C{3}^4\ast \delta {\ast }_{C}5\ast {\beta }^2+10{\ast }_C{5}^2\ast {\beta }^2\ast \gamma {\ast }_C{3}^2+16{\ast }_C{5}^2\ast \beta \ast {\gamma }^2{\ast }_C{3}^2-240{\ast }_C{3}^4\ast {\gamma }^2\ast \delta {\ast }_{C}5-3{\ast }_C{5}^3\ast \beta \ast \gamma \ast \alpha -{\beta }^2{\ast }_C{5}^3\ast \alpha +2400{\ast }_C{3}^6\ast {\delta }^2\ast \beta +2400{\ast }_C{3}^6\ast {\delta }^2\ast \gamma +10{\ast }_C{5}^3\ast \delta \ast {\alpha }^2+8\ast {\gamma }^3{\ast }_C{5}^2{\ast }_C{3}^2-2\ast {\gamma }^2{\ast }_C{5}^3\ast \alpha +2\ast {\beta }^3{\ast }_C{5}^2{\ast }_C{3}^2-360{\ast }_C{3}^4\ast \delta {\ast }_{C}5\ast \beta \ast \gamma +20{\ast }_C{5}^2\ast \delta \ast \alpha \ast \beta {\ast }_C{3}^2+(2/5)\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2\ast \beta \ast {\gamma }^2/\delta +(1/4)\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2\ast {\beta }^2\ast \gamma /\delta -9{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_{C}5\ast \beta \ast \gamma +30{\ast }_C{3}^2\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2))\ast \delta {\ast }_{C}5\ast \alpha +(1/5)\ast {\gamma }^3\ast (2\ast \gamma {\ast }_{C}5{+}_{C}5\ast \beta -40\ast \delta {\ast }_C{3}^2+\sqrt{(}4\ast {\gamma }^2{\ast }_C{5}^2+4\ast \gamma {\ast }_C{5}^2\ast \beta {+}_C{5}^2\ast {\beta }^2-40\ast \delta \ast \alpha {\ast }_C{5}^2)){\ast }_C{5}^2/\delta )$

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行波图

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

General Fifth order KdV equation traveling wave plot

参考文献

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