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Physical meaning of KdV equation

  1. Apr 20, 2015 #1
    Here is one of the KdV form

    u_t + u_x + uu_x + u_{xxx} = 0

    Where u is elevation, x is spatial variable, and t is time variable. The first two terms describe the linear water wave, the third term represent the nonlinear effect, and the last term is the dispersion.

    From what i understand, the nonlinear term explain the energy focusing that keeps the shape of the wave packet. But, how is u multiplied by u_x represents the energy focusing? For example, like in predator-prey model, the nonlinear term xy explain the interaction between the two species, where x and y are the number of predators and prey respectively.

    Also, how does the last term, the third derivative of u with respect to x, explain the dispersion which is the deformation of the waves?
     
  2. jcsd
  3. Apr 20, 2015 #2
    Sorry, It seems like i accidentally posted it twice, it is because of the low connection.
     
  4. Apr 20, 2015 #3
    Can anybody please help me to understand the physical interpretation of kdv eq.?
     
  5. Apr 23, 2015 #4
    [itex]uu_x = (\frac{1}{2}u^2)_x[/itex]

    so it represents convection of kinetic energy. There is a link with the (inviscid) Burgers equation.
     
  6. Apr 23, 2015 #5
    Thank you for replying.
    It gives me some hints to study more.

    This is how i understand it. Let u be the elevetion of wave. u^2 represents the interaction of waves which causes energy transfer among the waves. Am I correct?
     
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