奥斯特洛夫斯基方程

奥斯特洛夫斯基方程(Ostrovsky equation)是一个模拟海洋波浪的非线性偏微分方程：

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

解析解

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

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

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

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

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

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

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

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

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

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行波图

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

参考文献

1. *谷超豪 《孤立子理论中的达布变换及其几何应用》 上海科学技术出版社
2. *阎振亚著 《复杂非线性波的构造性理论及其应用》 科学出版社 2007年
3. 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
4. 王东明著 《消去法及其应用》 科学出版社 2002
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9. Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
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11. Dongming Wang, Elimination Practice,Imperial College Press 2004
12. David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
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