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## Homework Statement

my non linear pde is

du/dt = d/dx [3u

^{2}- d

^{2}u/dx

^{2}]

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 d

^{2}u/dt

^{2}and d

^{2}u/dx

^{2}

Which gave me in order as above, -cf' , f' , c

^{2}f'' , f''

## The Attempt at a Solution

But when i substitute these into the pde i get -cf' = d/dx[3f

^{2}- 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

Thank you