1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Miura transformation

  1. Aug 18, 2011 #1
    1. The problem statement, all variables and given/known data
    Show how the Miura transformation u = -(v2 + vx) connects the KdV ut + 6uux + uxxx = 0 to the modified KdV vt - 6v2vx + vxxx = 0
    Which of the following is true, and why?
    a) u solves the KdV if v solves the MKdV
    b) v solves the MKdV if u solves the KdV
    c) u solves the KdV if and only if v solves the MKdV.


    2. Relevant equations



    3. The attempt at a solution
    Let u = -(v2 + vx) therefore ut + 6uux + uxxx = vt + 6(-(v2 + vx))(2v+d/dx) + vxxx = 0, I'm lost after this bit, any ideas?
    I know a) is true because of application to the Miura transformation.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Miura transformation
  1. Laplace transform (Replies: 0)

  2. Fourier Transformation (Replies: 0)

  3. Fourier Transform (Replies: 0)

  4. Laplace Transform (Replies: 0)

Loading...