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

2012년 1월 14일 (토) 03:15 판

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

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.

\(u(x,t)=f(x-ct)\)로 두자.

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

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

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

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

@@ 17번째 줄: / 17번째 줄: @@
 *  numerically (Zabusky & Kruskal 1965).<br>
 ** interaction of two 1-soliton solutions
-** they discovered that solitons of differenct sizes interact cleanly
+** they discovered that solitons of different sizes interact cleanly
@@ 73번째 줄: / 73번째 줄: @@
 * 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%3A%2F%2Fkft.umcs.lublin.pl%2Fkmur%2Fdownload%2Fprezentacje%2Fsolitons_my.ppt
@@ 81번째 줄: / 82번째 줄: @@
 * [[파동 방정식|파동방정식]]
+* [[사인-고든 방정식]]