I need to solve the following nonlinear wave equation numerically
$$u_{tt} - (c^2+ u^2)u_{xx} =0$$ with initial conditions : $u(x,0) = 1$ if $|x|<L$ and $0$ otherwise, $u_t(x,0) = 0$.
What is the best method for solving it? I want to solve it using finite difference with matlab
Any help will be appreciated!