伊藤方程(Ito equation)是一个五阶非线性偏微分方程:[1]
解析解[编辑]
![{\displaystyle u(x,t)=_{C}2*sech(_{C}1+_{C}2*x-_{C}2^{5}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26eec595df89ca066a9c92403cac74be5d542fe4)
![{\displaystyle u(x,t)=_{C}3*JacobiDN(-_{C}2-_{C}3*x-(-6*_{C}3^{5}-_{C}3^{5}*_{C}1^{4}+6*_{C}3^{5}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8326c1cacd8aef3e83625e0f5bdf26fdab9254d7)
![{\displaystyle u(x,t)={\sqrt {(}}2)*_{C}3*JacobiCN(_{C}2+_{C}3*x-7*_{C}3^{5}*t,(1/2)*sqrt(2))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/743fa4f3f19134fce62166d1947f7685b61ec2c6)
![{\displaystyle u(x,t)=-I*_{C}2*cot(_{C}1+_{C}2*x-6*_{C}2^{5}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ac726358bde1eea13e1c24dd607b57c38625e39d)
![{\displaystyle u(x,t)=-I*_{C}2*tan(_{C}1+_{C}2*x-6*_{C}2^{5}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/d527831a7ca3c0ef9d9ad8a1636e1913fc31534e)
![{\displaystyle u(x,t)=-I*_{C}3*JacobiNS(-_{C}2-_{C}3*x-(-_{C}3^{5}*_{C}1^{4}-_{C}3^{5}-4*_{C}3^{5}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3a895fe670c074dc05f573ecc2d8122c09c1beef)
![{\displaystyle u(x,t)=I*_{C}2*csc(_{C}1+_{C}2*x-_{C}2^{5}*t)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ab8a5a4177ea79ccdff5f3a20f4123a4bf1a32cf)
![{\displaystyle u(x,t)=(2*I)*_{C}3*JacobiND(_{C}2+_{C}3*x-28*_{C}3^{5}*t,sqrt(2))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f9eb42c1add82eec761a47e702c36468441c5cda)
![{\displaystyle u(x,t)=-I*sqrt(2)*_{C}3*JacobiNC(_{C}2+_{C}3*x-7*_{C}3^{5}*t,(1/2)*sqrt(2))}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a1af6d2238d7e540484395afc5668c12100cee81)
![{\displaystyle u(x,t)=-2*_{C}3*JacobiSN(_{C}2+_{C}3*x-28*_{C}3^{5}*t,I)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/79cfc7de7ba46054f5190ce4592b86ce589b7f43)
![{\displaystyle u(x,t)=-{\sqrt {(}}1-_{C}1^{2})*_{C}3*JacobiND(-_{C}2-_{C}3*x-(-6*_{C}3^{5}-_{C}3^{5}*_{C}1^{4}+6*_{C}3^{5}*_{C}1^{2})*t,_{C}1)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/31274e639b515d6defd0090fed341186db10b7a0)
行波图[编辑]
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
Ito equation traveling wave plot
|
参考文献[编辑]
- ^ 李志斌编著 《非线性数学物理方程的行波解》 138页 科学出版社 2008
- *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
- *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
- 李志斌编著 《非线性数学物理方程的行波解》 科学出版社
- 王东明著 《消去法及其应用》 科学出版社 2002
- *何青 王丽芬编著 《Maple 教程》 科学出版社 2010 ISBN 9787030177445
- Graham W. Griffiths William E.Shiesser Traveling Wave Analysis of Partial Differential p135 Equations Academy Press
- Richard H. Enns George C. McCGuire, Nonlinear Physics Birkhauser,1997
- Inna Shingareva, Carlos Lizárraga-Celaya,Solving Nonlinear Partial Differential Equations with Maple Springer.
- Eryk Infeld and George Rowlands,Nonlinear Waves,Solitons and Chaos,Cambridge 2000
- Saber Elaydi,An Introduction to Difference Equationns, Springer 2000
- Dongming Wang, Elimination Practice,Imperial College Press 2004
- David Betounes, Partial Differential Equations for Computational Science: With Maple and Vector Analysis Springer, 1998 ISBN 9780387983004
- George Articolo Partial Differential Equations & Boundary Value Problems with Maple V Academic Press 1998 ISBN 9780120644759