코테베그-드 브리스 방정식(KdV equation)

이 항목의 스프링노트 원문주소

• 솔리톤

 

 

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 different 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)

• 
• 1-soliton 해의 유도

로 두자.

 

 

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
• http%3A%2F%2Fkft.umcs.lublin.pl%2Fkmur%2Fdownload%2Fprezentacje%2Fsolitons_my.ppt

 

 

관련된 항목들

• 파동방정식
• 사인-고든 방정식

 

 

수학용어번역

• 단어사전 http://www.google.com/dictionary?langpair=en|ko&q=

• 발음사전

  •  http://www.forvo.com/search/Korteweg
  • http://www.forvo.com/search/de%20vries/nl/

• 대한수학회 수학 학술 용어집

  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/솔리톤
• http://en.wikipedia.org/wiki/John_Scott_Russell

 

 

리뷰

• An Introduction to Solitons ,Alex Kasman