1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Solving a non linear pde using a function

  1. Oct 27, 2011 #1
    I have the non linear pde

    du/dt = d/dx [3 u^2 - d^2u/dx^2]

    the question supposes that there is a solution u(x,t) = f(x-ct) where c is constant and f(y) for y=x-ct satisfies f tends to 0, f' tends to zero and f'' tends to zero but y tends to + or - infinity.

    so i have tried to reduce the above equation to an ode, i have to show that a family of solutions of the pde are given by u(x,t) = -c/2 sech^2 [ c^{1/2} /2 (x-ct)]

    i find
    du/dt = -cf'
    du/dx = f'
    d^2u/dt^2 = c^2 f''
    d^2u/dx^2 = f''

    but when substituting these into the pde and simplifying i get

    f'''-cf'-6f'=0 so f''' = (6+c)f'

    is it possible to 'cancel the derivatives' so that f''=(6+c)f and f'=(6+c) ?

    im really stuck on this question
    any help would really be appreciated

  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted