I really need help to solve this problem:
Find all simple wave solutions of the equation: $$u_{tt} = (1+u_x)^2u_{xx}$$ with $u(x,0)=h(x)$. [Hint: write above equation as a first order system for the vector $v =(u_x, u_t)$ and find the solutions with $u_x=\theta, u_t=F(\theta)$].
Here is a answer for this : $u=\pm \frac{1}{2}\theta ^2 + h(x \mp (1+\theta)t) +ct$, where $c$ is constant and $\theta$ is solution of $\theta = h'(x \pm (1+\theta )t)$.
I have no idea how to solve this. Any help I really appreciate. Thanks