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.
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 I am not sure actually helps
Could someone please tell me if i am using the correct method or if i have done it completely wrong