"코테베그-드 브리스 방정식(KdV equation)"의 두 판 사이의 차이

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==이 항목의 스프링노트 원문주소==
 
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* [[코테베그-드 브리스 방정식(KdV equation)|솔리톤]]
 
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==개요==
 
==개요==
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* any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)
 
* any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)
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* Solitons were discovered experimentally (Russell 1844)
 
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*  analytically (Korteweg & de Vries, 1895)<br>
 
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** modelling of Russell's discovery
 
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** 1-soliton solution
 
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*  numerically (Zabusky & Kruskal 1965).<br>
 
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** interaction of two 1-soliton solutions
 
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** they discovered that solitons of different sizes interact cleanly
 
  
 
 
 
 
57번째 줄: 40번째 줄:
  
 
==역사==
 
==역사==
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* Solitons were discovered experimentally (Russell 1844)
 +
*  analytically (Korteweg & de Vries, 1895)<br>
 +
** modelling of Russell's discovery
 +
** 1-soliton solution
 +
*  numerically (Zabusky & Kruskal 1965).<br>
 +
** interaction of two 1-soliton solutions
 +
** they discovered that solitons of different sizes interact cleanly
 
* [http://www.ma.hw.ac.uk/%7Echris/scott_russell.html John Scott Russell and the solitary wave]
 
* [http://www.ma.hw.ac.uk/%7Echris/scott_russell.html John Scott Russell and the solitary wave]
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=
 
* http://www.google.com/search?hl=en&tbs=tl:1&q=

2013년 1월 25일 (금) 16:46 판

개요

  • any localized nonlinear wave which interacts with another (arbitrary) local disturbance and always regains asymptotically its exact initial shape and velocity (allowing for a possible phase shift)

 

 

러셀(John Scott Russell)의 관찰 

  • Using a wave tank, he demonstrated four facts
    • First, solitary waves have a hyperbolic secant shape.
    • Second, a sufficiently large initial mass of water produces two or more independent solitary waves.
    • Third, solitary waves cross each other “without change of any kind.”
    • Finally, a wave of height h and traveling in a channel of depth d has a velocity given by the expression (where g is the acceleration of gravity), implying that a large amplitude solitary wave travels faster than one of low amplitude.

 

 

 

코테베그-드 브리스 방정식 (KdV equation)

  • \(u_{xxx}=u_t+6uu_x\)
  • 1-soliton 해의 유도

\(u(x,t)=f(x-ct)\)로 두자.

\(f'''= 6ff'-cf'\)

\(f''=3f^2-cf+b\)

\(f''f'=(3f^2-cf+b)f'\)

\(\frac{1}{2}(f')^2=f^3-\frac{c}{2}f^2+bf+a\)

 

 

역사

 

 

메모

 

 

관련된 항목들

 

 

수학용어번역

 

 

사전 형태의 자료

 

 

리뷰

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