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

수학노트
둘러보기로 가기 검색하러 가기
51번째 줄: 51번째 줄:
  
 
<math>\frac{1}{2}(f')^2=f^3-\frac{c}{2}f^2+bf+a</math>
 
<math>\frac{1}{2}(f')^2=f^3-\frac{c}{2}f^2+bf+a</math>
−
 
−
 
 
−
 
−
 
 
−
 
−
<h5>재미있는 사실</h5>
 
−
 
−
 
 
−
 
−
* Math Overflow http://mathoverflow.net/search?q=
 
−
* 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
 
  
 
 
 
 
81번째 줄: 70번째 줄:
 
<h5>메모</h5>
 
<h5>메모</h5>
  
−
http://docs.google.com/viewer?a=v&q=cache:dWzyEHjy6JsJ:kft.umcs.lublin.pl/kmur/download/prezentacje/solitons_my.ppt+soliton+ppt&hl=ko&gl=us&pid=bl&srcid=ADGEESi5cLc2o4aGrXBSQM9i6u_2MalwSshBjfJzoGv4FsWRYcdUPcXNvQhwXLG6RpQsnwlT0f5-UGFkKVJr14cvsGjY2zDOhqLc1bwORnRHVYCsbv08l5dgO9xFhgNO8D1Vg29R4SAJ&sig=AHIEtbRDvlbVm-kiG23Az3C2olliRZdB8Q
+
* http://docs.google.com/viewer?a=v&q=cache:dWzyEHjy6JsJ:kft.umcs.lublin.pl/kmur/download/prezentacje/solitons_my.ppt+soliton+ppt&hl=ko&gl=us&pid=bl&srcid=ADGEESi5cLc2o4aGrXBSQM9i6u_2MalwSshBjfJzoGv4FsWRYcdUPcXNvQhwXLG6RpQsnwlT0f5-UGFkKVJr14cvsGjY2zDOhqLc1bwORnRHVYCsbv08l5dgO9xFhgNO8D1Vg29R4SAJ&sig=AHIEtbRDvlbVm-kiG23Az3C2olliRZdB8Q
−
 
+
* http://www.springerlink.com/content/gr665351h46628j6/fulltext.html
−
http://www.springerlink.com/content/gr665351h46628j6/fulltext.html
+
* [http://people.seas.harvard.edu/%7Ejones/solitons/pdf/025.pdf http://people.seas.harvard.edu/~jones/solitons/pdf/025.pdf]
−
 
 
−
[http://people.seas.harvard.edu/%7Ejones/solitons/pdf/025.pdf http://people.seas.harvard.edu/~jones/solitons/pdf/025.pdf]
 
  
 
 
 
 
102번째 줄: 89번째 줄:
  
 
* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=
 
* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=
−
* 발음사전 http://www.forvo.com/search/
+
* 발음사전 http://www.forvo.com/search/Korteweg
 
* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
 
* [http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=&fstr= 대한수학회 수학 학술 용어집]<br>
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
 
** http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=

2012년 1월 11일 (수) 17:28 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.

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

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

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

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

 

 

역사

 

 

메모

 

 

관련된 항목들

 

 

수학용어번역

 

 

사전 형태의 자료

 

 

리뷰

 

 

관련논문

 

 

관련도서

 

 

관련기사

 

 

링크
원본 주소 "https://wiki.mathnt.net/index.php?title=코테베그-드_브리스_방정식(KdV_equation)&oldid=19642"