"코테베그-드 브리스 방정식(KdV equation)"의 두 판 사이의 차이
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(피타고라스님이 이 페이지의 이름을 코테베그-드 브리스 방정식(KdV equation)로 바꾸었습니다.) |
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| − | <h5> | + | <h5>코테베그-드 브리스 방정식 (KdV equation)</h5> |
* <math>u_{xxx}=u_t+6uu_x</math> | * <math>u_{xxx}=u_t+6uu_x</math> | ||
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* 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | * 단어사전 http://www.google.com/dictionary?langpair=en|ko&q= | ||
| − | * | + | * 발음사전<br> |
| + | ** http://www.forvo.com/search/Korteweg | ||
| + | ** http://www.forvo.com/search/de%20vries/nl/ | ||
* [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= | ||
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* [http://ko.wikipedia.org/wiki/%EC%86%94%EB%A6%AC%ED%86%A4 http://ko.wikipedia.org/wiki/솔리톤] | * [http://ko.wikipedia.org/wiki/%EC%86%94%EB%A6%AC%ED%86%A4 http://ko.wikipedia.org/wiki/솔리톤] | ||
* http://en.wikipedia.org/wiki/John_Scott_Russell | * http://en.wikipedia.org/wiki/John_Scott_Russell | ||
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* [http://kasmana.people.cofc.edu/SOLITONPICS/index.html An Introduction to Solitons] ,Alex Kasman | * [http://kasmana.people.cofc.edu/SOLITONPICS/index.html An Introduction to Solitons] ,Alex Kasman | ||
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2012년 1월 12일 (목) 08:21 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.
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
- John Scott Russell and the solitary wave
- http://www.google.com/search?hl=en&tbs=tl:1&q=
- Earliest Known Uses of Some of the Words of Mathematics
- Earliest Uses of Various Mathematical Symbols
- 수학사연표
메모
- 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://people.seas.harvard.edu/~jones/solitons/pdf/025.pdf
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
리뷰
- An Introduction to Solitons ,Alex Kasman