코테베그-드 브리스 방정식(KdV equation)
http://bomber0.myid.net/ (토론)님의 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
- Math Overflow http://mathoverflow.net/search?q=
- 네이버 지식인 http://kin.search.naver.com/search.naver?where=kin_qna&query=
역사
- 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
관련된 항목들
수학용어번역
- 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
- 발음사전 http://www.forvo.com/search/
- 대한수학회 수학 학술 용어집
- 남·북한수학용어비교
- 대한수학회 수학용어한글화 게시판
사전 형태의 자료
- http://ko.wikipedia.org/wiki/솔리톤
- http://en.wikipedia.org/wiki/
- http://www.proofwiki.org/wiki/
- http://www.wolframalpha.com/input/?i=
- The Online Encyclopaedia of Mathematics
- NIST Digital Library of Mathematical Functions
- The On-Line Encyclopedia of Integer Sequences
관련논문
관련도서
- 도서내검색
- 도서검색
관련기사
- 네이버 뉴스 검색 (키워드 수정)