
#1
Sep607, 02:21 AM

P: 320

Hi all.
Can someone explain me physically why we need to deal with wave packets in water waves? I know the the nonlinear schrodinger equations deals with wave packets in water wave. But why bother dealing with wave packets? For the KdV equation, the concept of wave packets is not needed, why? What so special about wave packets? Please help. 



#2
Sep607, 03:41 AM

P: 981

Schroedinger equation deals with water? That's new to me.




#3
Sep707, 12:53 AM

P: 320

Please help. 



#4
Sep707, 12:59 AM

P: 2,050

Why wave packets?
They're special in that they represent particles?




#5
Sep707, 01:10 AM

Emeritus
Sci Advisor
PF Gold
P: 11,154





#6
Sep707, 11:41 AM

Sci Advisor
P: 2,341

I like the undergraduate level introduction by P. G. Drazin and R. S. Johnson, Solitons: an Introduction, Cambridge University Press, 1989. If you follow this up, you will see how the usual Schroedinger equation plays a role in the famous inversescattering transform method of solving the KdV, a famous soliton equation, which arises as an approximation of water waves under certain circumstances. This spawned a great deal of work, including analysis of related PDEs, such as the mKdV, the BBM equation, the CamassaHolm equation, etc. (the latter also arises as approximations of water waves and includes idealized "breaking of waves"; see math.AP/0709.0905). The nonlinear Schroedinger equation is a nonlinear generalization of the Schroedinger equation which itself has some aspects of a soliton equation. The sineGordon equation is another well known nonlinear PDE which has some solitonlike solutions. You can search the arXiv to find many recent papers discussing current research in this area. Needless to say, you will need a strong background in differential equations to follow this research. 



#7
Sep907, 11:36 AM

P: 320

How does KdV equation deal with wave packets?



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