奧斯特洛夫斯基方程

奧斯特洛夫斯基方程(Ostrovsky equation)是一個模擬海洋波浪的非線性偏微分方程：

$u^{2}*u_{t}-u_{x}*u_{xt}+u*u_{xxt}=0$

解析解

$u(x,t)=-6*_{C}2^{2}*csch(_{C}1+_{C}2*x+_{C}3*t)^{2}$

$u(x,t)=-6*_{C}2^{2}*sec(_{C}1+_{C}2*x+_{C}3*t)^{2}$

$u(x,t)=6*_{C}2^{2}*sech(_{C}1+_{C}2*x+_{C}3*t)^{2}$

$u(x,t)=_{C}5+6*_{C}3^{2}*JacobiDN(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt((3*_{C}3^{2}+_{C}5)*(_{C}5^{2}+12*_{C}3^{4}+8*_{C}5*_{C}3^{2}))/((3*_{C}3^{2}+_{C}5)*_{C}3))^{2}$

$u(x,t)=_{C}5-6*_{C}3^{2}*JacobiNS(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt((-3*_{C}3^{2}+_{C}5)*_{C}5*(_{C}5-4*_{C}3^{2}))/((-3*_{C}3^{2}+_{C}5)*_{C}3))^{2}$

$u(x,t)=_{C}6-6*_{C}4^{2}*WeierstrassP(_{C}3+_{C}4*x+_{C}5*t,(1/3)*_{C}6^{2}/_{C}4^{4},_{C}1)$

$u(x,t)=_{C}5-(3/2)*_{C}5*(4*_{C}3^{2}+_{C}5)*JacobiND(_{C}2+_{C}3*x+_{C}4*t,(1/2)*sqrt((3*_{C}3^{2}+_{C}5)*(_{C}5^{2}+12*_{C}3^{4}+8*_{C}5*_{C}3^{2}))/((3*_{C}3^{2}+_{C}5)*_{C}3))^{2}/(3*_{C}3^{2}+_{C}5)$

$u(x,t)=2*_{C}2^{2}-6*_{C}2^{2}*coth(_{C}1+_{C}2*x+_{C}3*t)^{2}$

$u(x,t)=(2-4*_{C}1^{2}-2*sqrt(1-_{C}1^{2}+_{C}1^{4}))*_{C}3^{2}+(-6*_{C}3^{2}+6*_{C}3^{2}*_{C}1^{2})*JacobiNC(_{C}2+_{C}3*x+_{C}4*t,_{C}1)^{2}$

${\displaystyle }$

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行波圖

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

Ostrovsky equation traveling wave plot

參考文獻

1. *谷超豪 《孤立子理論中的達布變換及其幾何應用》 上海科學技術出版社
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4. 王東明著 《消去法及其應用》 科學出版社 2002
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9. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
10. Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
11. Dongming Wang, Elimination Practice,Imperial College Press 2004
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