# How to solve this non-linear PDE?

1. Sep 15, 2009

### aminfar

I am new to non-linear PDEs. So I tried to solve it, but I stuck in the beginning.

$$U^2_xU_t - 1 = 0$$

$$U(x, 0) = x$$

2. Oct 5, 2009

### gato_

The equation admits a separation of variables, and the solution can be written as U(x,t)=f(x)+g(t). Inserting this, you get f'(x)^2=1/g'(t)=constant. The solution can then be checked to be U=x+t