泽田-小寺方程

泽田-小寺方程(Sawada-Kotera equation)是一个非线性偏微分方程：

$U_{t}+45*(U)^{2}*U_{x}+15*U_{x}*U_{xx}+15*U*U_{xxx}+U_{xxxxx}=0$

解析解

$u(x,t)=-(8/3)*_{C}2^{2}-4*_{C}2^{2}*cot(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=-(8/3)*_{C}2^{2}-4*_{C}2^{2}*tan(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=-(4/3)*_{C}2^{2}-4*_{C}2^{2}*csch(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=-(4/3)*_{C}2^{2}+4*_{C}2^{2}*sech(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=(4/3)*_{C}2^{2}-4*_{C}2^{2}*csc(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=(4/3)*_{C}2^{2}-4*_{C}2^{2}*sec(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=(8/3)*_{C}2^{2}-4*_{C}2^{2}*coth(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=(8/3)*_{C}2^{2}-4*_{C}2^{2}*tanh(_{C}1+_{C}2*x-16*_{C}2^{5}*t)^{2}$

$u(x,t)=-(8/3)*_{C}3^{2}+(4/3)*_{C}3^{2}*_{C}1^{2}+4*_{C}3^{2}*JacobiDN(-_{C}2-_{C}3*x-(-16*_{C}3^{5}+16*_{C}3^{5}*_{C}1^{2}-16*_{C}3^{5}*_{C}1^{4})*t,_{C}1)^{2}$

$u(x,t)=-(8/3)*_{C}3^{2}*_{C}1^{2}+(4/3)*_{C}3^{2}+(-4*_{C}3^{2}+4*_{C}3^{2}*_{C}1^{2})*JacobiNC(-_{C}2-_{C}3*x-(-16*_{C}3^{5}+16*_{C}3^{5}*_{C}1^{2}-16*_{C}3^{5}*_{C}1^{4})*t,_{C}1)^{2}$

$u(x,t)=(4/3)*_{C}3^{2}*_{C}1^{2}+(4/3)*_{C}3^{2}-4*_{C}3^{2}*_{C}1^{2}*JacobiSN(-_{C}2-_{C}3*x-(-16*_{C}3^{5}+16*_{C}3^{5}*_{C}1^{2}-16*_{C}3^{5}*_{C}1^{4})*t,_{C}1)^{2}$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

${\displaystyle }$

行波图

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

Sawada-Kotera equation traveling wave plot

参考文献

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3. 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
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