Non linear pde need to change it to an ode

  • Thread starter maggie56
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Homework Statement


my non linear pde is
du/dt = d/dx [3u2 - d2u/dx2 ]
The question says to let u(x,t) = f(x-ct)
Where the function f tends to 0, f' tends to 0 and f'' tends to 0 but the (x-ct) tends to positive or negative infinity.

Homework Equations


i thought the solution was to find du/dt du/dx d2u/dt2 and d2u/dx2
Which gave me in order as above, -cf' , f' , c2f'' , f''


The Attempt at a Solution



But when i substitute these into the pde i get -cf' = d/dx[3f2 - f"] which im not sure actually helps

Could someone please tell me if i am using the correct method or if i have done it completely wrong

Thank you
 

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