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

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<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 스프링노트 원문주소</h5>
 
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">이 항목의 스프링노트 원문주소</h5>
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* [[코테베그-드 브리스 방정식(KdV equation)|솔리톤]]
  
 
 
 
 
6번째 줄: 8번째 줄:
  
 
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
 
<h5 style="margin: 0px; line-height: 3.428em; color: rgb(34, 61, 103); font-family: 'malgun gothic',dotum,gulim,sans-serif; font-size: 1.166em; background-position: 0px 100%;">개요</h5>
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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)
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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 differenct sizes interact cleanly
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<h5>러셀(John Scott Russell)의 관찰 </h5>
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*  Using a wave tank, he demonstrated four facts<br>
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** First, solitary waves have a hyperbolic secant shape.
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** Second, a sufficiently large initial mass of water produces two or more independent solitary waves.
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** Third, solitary waves cross each other “without change of any kind.”
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** 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.
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2011년 3월 13일 (일) 11:32 판

이 항목의 스프링노트 원문주소

 

 

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)
  • Solitons were discovered experimentally (Russell 1844)
  • analytically (Korteweg & de Vries, 1895)
    • modelling of Russell's discovery
    • 1-soliton solution
  • numerically (Zabusky & Kruskal 1965).
    • interaction of two 1-soliton solutions
    • they discovered that solitons of differenct sizes interact cleanly

 

 

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.

 

 

 

코르테베그-드 브리스 방정식 (KdV equation)
  • \(u_{xxx}=u_t+6uu_x\)
  • 1-soliton 해의 유도

\(u(x,t)=f(x-ct)\)로 두자.

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

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

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

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

 

 

재미있는 사실

 

 

 

역사

 

 

 

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관련된 항목들

 

 

수학용어번역

 

 

사전 형태의 자료

 

 

관련논문

 

 

관련도서

 

 

관련기사

 

 

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