库普-库珀施密特方程 行波解 参考文献 导航菜单编
阿多米安分解法Bäcklund变换C-K直接约化法达布变换Domion结构高阶约束流反散射法非古典李对称分離變數法加德纳变换古典李对称广田法霍普夫-科尔变换换位表示混合指数法Lax 对Liouville可积龙格-库塔法Miura变换Panlevé分析齐次平衡法Riccati方程展开法摄动理论Tanh 函数展开法特征线法屠格式理论有限差分法线条法
偏微分方程孤立子
Maple
库普-库珀施密特方程(Kaup-Kupershmidt Equation)是一个非线性偏微分方程:[1]
∂4u(x,t)∂x4+∂u(x,t)∂x+45(∂u(x,t)∂x∗u(x,t)2−(75/2)∗∂2u(x,t)∂x2∗∂u(x,t)∂x−15∗u(x,t)∗∂3u(x,t)∂x3{displaystyle {frac {partial ^{4}u(x,t)}{partial x^{4}}}+{frac {partial u(x,t)}{partial x}}+45({frac {partial u(x,t)}{partial x}}*u(x,t)^{2}-(75/2)*{frac {partial ^{2}u(x,t)}{partial x^{2}}}*{frac {partial u(x,t)}{partial x}}-15*u(x,t)*{frac {partial ^{3}u(x,t)}{partial x^{3}}}}
行波解
利用Maple软件包TWSolution,随所选定展开函数不同,可得多种行波解[2]
- tanh 展开
g[2]:=u(x,t)=−(2/3)∗(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗tanh(C1+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[2]:={u(x,t)=-(2/3)*(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*tanh(_{C}1+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[3]:=u(x,t)=−(2/3)∗(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗tanh(C1+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[3]:={u(x,t)=-(2/3)*(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*tanh(_{C}1+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[4]:=u(x,t)=−(2/3)∗((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗tanh(C1+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[4]:={u(x,t)=-(2/3)*((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*tanh(_{C}1+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[5]:=u(x,t)=−(2/3)∗((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗tanh(C1+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[5]:={u(x,t)=-(2/3)*((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*tanh(_{C}1+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[6]:=u(x,t)=−(4/3)∗(−(1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗(−(1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2∗tanh(C1+(−(1/44)∗sqrt(2)∗11(3/4)−(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[6]:={u(x,t)=-(4/3)*(-(1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*(-(1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*tanh(_{C}1+(-(1/44)*sqrt(2)*11^{(}3/4)-(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[7]:=u(x,t)=−(4/3)∗(−(1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗(−(1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2∗tanh(C1+(−(1/44)∗sqrt(2)∗11(3/4)+(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[7]:={u(x,t)=-(4/3)*(-(1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*(-(1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*tanh(_{C}1+(-(1/44)*sqrt(2)*11^{(}3/4)+(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[8]:=u(x,t)=−(4/3)∗((1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗((1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2∗tanh(C1+((1/44)∗sqrt(2)∗11(3/4)−(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[8]:={u(x,t)=-(4/3)*((1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*((1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*tanh(_{C}1+((1/44)*sqrt(2)*11^{(}3/4)-(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[9]:=u(x,t)=−(4/3)∗((1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗((1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2∗tanh(C1+((1/44)∗sqrt(2)∗11(3/4)+(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[9]:={u(x,t)=-(4/3)*((1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*((1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*tanh(_{C}1+((1/44)*sqrt(2)*11^{(}3/4)+(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
.mw-parser-output .gallery-mod{background:transparent;margin-top:0.5em}.mw-parser-output .gallery-mod-collapsible{width:100%}.mw-parser-output .gallery-mod-center{margin:0 auto}.mw-parser-output .gallery-mod-title{text-align:center;font-weight:bold}.mw-parser-output .gallery-mod-box{float:left;border-collapse:collapse;margin:3px}.mw-parser-output .gallery-mod-box .thumb{border:1px solid #ccc;background-color:#F8F8F8;padding:0;text-align:center}.mw-parser-output tr.gallery-mod-text{vertical-align:top}.mw-parser-output tr.gallery-mod-text .core{display:block;font-size:small;padding:0}.mw-parser-output .gallery-mod-text .caption{line-height:1.25em;padding:6px 6px 1px 6px;margin:0;border:none;border-width:0;text-align:left}.mw-parser-output .gallery-mod-footer{text-align:right;font-size:80%;line-height:1em}
- JacobiSN 展开
g[2]:=u(x,t)=−(1/2)∗C32−(1/6)∗sqrt(−3∗C34−4)+((1/2)∗C32+(1/2)∗sqrt(−3∗C34−4))∗JacobiSN(C2+C3∗x+C4∗t,(1/2)∗sqrt(2∗C32+2∗sqrt(−3∗C34−4))/C3)2{displaystyle g[2]:={u(x,t)=-(1/2)*_{C}3^{2}-(1/6)*sqrt(-3*_{C}3^{4}-4)+((1/2)*_{C}3^{2}+(1/2)*sqrt(-3*_{C}3^{4}-4))*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt(2*_{C}3^{2}+2*sqrt(-3*_{C}3^{4}-4))/_{C}3)^{2}}}
g[3]:=u(x,t)=−(1/2)∗C32+(1/6)∗sqrt(−3∗C34−4)+((1/2)∗C32−(1/2)∗sqrt(−3∗C34−4))∗JacobiSN(C2+C3∗x+C4∗t,(1/2)∗sqrt(2∗C32−2∗sqrt(−3∗C34−4))/C3)2{displaystyle g[3]:={u(x,t)=-(1/2)*_{C}3^{2}+(1/6)*sqrt(-3*_{C}3^{4}-4)+((1/2)*_{C}3^{2}-(1/2)*sqrt(-3*_{C}3^{4}-4))*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt(2*_{C}3^{2}-2*sqrt(-3*_{C}3^{4}-4))/_{C}3)^{2}}}
g[4]:=u(x,t)=−4∗C32−(2/33)∗sqrt(−1452∗C34−11)+(4∗C32+(2/11)∗sqrt(−1452∗C34−11))∗JacobiSN(C2+C3∗x+C4∗t,(1/22)∗sqrt(242∗C32+11∗sqrt(−1452∗C34−11))/C3)2{displaystyle g[4]:={u(x,t)=-4*_{C}3^{2}-(2/33)*sqrt(-1452*_{C}3^{4}-11)+(4*_{C}3^{2}+(2/11)*sqrt(-1452*_{C}3^{4}-11))*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/22)*sqrt(242*_{C}3^{2}+11*sqrt(-1452*_{C}3^{4}-11))/_{C}3)^{2}}}
g[5]:=u(x,t)=−4∗C32+(2/33)∗sqrt(−1452∗C34−11)+(4∗C32−(2/11)∗sqrt(−1452∗C34−11))∗JacobiSN(C2+C3∗x+C4∗t,(1/22)∗sqrt(242∗C32−11∗sqrt(−1452∗C34−11))/C3)2{displaystyle g[5]:={u(x,t)=-4*_{C}3^{2}+(2/33)*sqrt(-1452*_{C}3^{4}-11)+(4*_{C}3^{2}-(2/11)*sqrt(-1452*_{C}3^{4}-11))*JacobiSN(_{C}2+_{C}3*x+_{C}4*t,(1/22)*sqrt(242*_{C}3^{2}-11*sqrt(-1452*_{C}3^{4}-11))/_{C}3)^{2}}}
- sech 展开
g[2]:=u(x,t)=(1/3)∗(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2−(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗sech(C1+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[2]:={u(x,t)=(1/3)*(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}-(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*sech(_{C}1+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[3]:=u(x,t)=(1/3)∗(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2−(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗sech(C1+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[3]:={u(x,t)=(1/3)*(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}-(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*sech(_{C}1+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[4]:=u(x,t)=(1/3)∗((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2−((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗sech(C1+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[4]:={u(x,t)=(1/3)*((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}-((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*sech(_{C}1+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[5]:=u(x,t)=(1/3)∗((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2−((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗sech(C1+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[5]:={u(x,t)=(1/3)*((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}-((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*sech(_{C}1+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[6]:=u(x,t)=(2/3)∗(−(1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2−2∗(−(1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2∗sech(C1+(−(1/44)∗sqrt(2)∗11(3/4)−(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[6]:={u(x,t)=(2/3)*(-(1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}-2*(-(1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sech(_{C}1+(-(1/44)*sqrt(2)*11^{(}3/4)-(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[7]:=u(x,t)=(2/3)∗(−(1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2−2∗(−(1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2∗sech(C1+(−(1/44)∗sqrt(2)∗11(3/4)+(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[7]:={u(x,t)=(2/3)*(-(1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}-2*(-(1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sech(_{C}1+(-(1/44)*sqrt(2)*11^{(}3/4)+(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[8]:=u(x,t)=(2/3)∗((1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2−2∗((1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2∗sech(C1+((1/44)∗sqrt(2)∗11(3/4)−(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[8]:={u(x,t)=(2/3)*((1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}-2*((1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sech(_{C}1+((1/44)*sqrt(2)*11^{(}3/4)-(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[9]:=u(x,t)=(2/3)∗((1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2−2∗((1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2∗sech(C1+((1/44)∗sqrt(2)∗11(3/4)+(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[9]:={u(x,t)=(2/3)*((1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}-2*((1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sech(_{C}1+((1/44)*sqrt(2)*11^{(}3/4)+(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
- sec、coth 展开
g[2]:=u(x,t)=−(1/3)∗(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗sec(C1+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[2]:={u(x,t)=-(1/3)*(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*sec(_{C}1+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[3]:=u(x,t)=−(1/3)∗(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗sec(C1+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[3]:={u(x,t)=-(1/3)*(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*sec(_{C}1+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[4]:=u(x,t)=−(1/3)∗((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗sec(C1+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[4]:={u(x,t)=-(1/3)*((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*sec(_{C}1+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[5]:=u(x,t)=−(1/3)∗((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗sec(C1+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[5]:={u(x,t)=-(1/3)*((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*sec(_{C}1+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[6]:=u(x,t)=−(2/3)∗(−(1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗(−(1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2∗sec(C1+(−(1/44)∗sqrt(2)∗11(3/4)−(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[6]:={u(x,t)=-(2/3)*(-(1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*(-(1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sec(_{C}1+(-(1/44)*sqrt(2)*11^{(}3/4)-(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[7]:=u(x,t)=−(2/3)∗(−(1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗(−(1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2∗sec(C1+(−(1/44)∗sqrt(2)∗11(3/4)+(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[7]:={u(x,t)=-(2/3)*(-(1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*(-(1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sec(_{C}1+(-(1/44)*sqrt(2)*11^{(}3/4)+(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[8]:=u(x,t)=−(2/3)∗((1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗((1/22)∗sqrt(2)∗11(3/4)−(1/22∗I)∗sqrt(2)∗11(3/4))2∗sec(C1+((1/44)∗sqrt(2)∗11(3/4)−(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[8]:={u(x,t)=-(2/3)*((1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*((1/22)*sqrt(2)*11^{(}3/4)-(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sec(_{C}1+((1/44)*sqrt(2)*11^{(}3/4)-(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[9]:=u(x,t)=−(2/3)∗((1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2+2∗((1/22)∗sqrt(2)∗11(3/4)+(1/22∗I)∗sqrt(2)∗11(3/4))2∗sec(C1+((1/44)∗sqrt(2)∗11(3/4)+(1/44∗I)∗sqrt(2)∗11(3/4))∗x+C3∗t)2{displaystyle g[9]:={u(x,t)=-(2/3)*((1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}+2*((1/22)*sqrt(2)*11^{(}3/4)+(1/22*I)*sqrt(2)*11^{(}3/4))^{2}*sec(_{C}1+((1/44)*sqrt(2)*11^{(}3/4)+(1/44*I)*sqrt(2)*11^{(}3/4))*x+_{C}3*t)^{2}}}
g[10]:=u(x,t)=−(2/3)∗(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗coth(C1+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[10]:={u(x,t)=-(2/3)*(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*coth(_{C}1+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
- csch 展开
u(x,t)=C4{displaystyle {u(x,t)=_{C}4}}
g[2]:=u(x,t)=(1/3)∗(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗csch(C1+(−(1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[2]:={u(x,t)=(1/3)*(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*csch(_{C}1+(-(1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[3]:=u(x,t)=(1/3)∗(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗csch(C1+(−(1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[3]:={u(x,t)=(1/3)*(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*csch(_{C}1+(-(1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[4]:=u(x,t)=(1/3)∗((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))2∗csch(C1+((1/2)∗sqrt(2)−(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[4]:={u(x,t)=(1/3)*((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))^{2}*csch(_{C}1+((1/2)*sqrt(2)-(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
g[5]:=u(x,t)=(1/3)∗((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))2∗csch(C1+((1/2)∗sqrt(2)+(1/2∗I)∗sqrt(2))∗x+C3∗t)2{displaystyle g[5]:={u(x,t)=(1/3)*((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))^{2}*csch(_{C}1+((1/2)*sqrt(2)+(1/2*I)*sqrt(2))*x+_{C}3*t)^{2}}}
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