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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