Nonlinear second order partial differential equation Integration

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I have the following nonlinear second order partial differential equation:

$\dfrac{\partial^2}{\partial t^2} \log(1 + u) = \nabla^2 u.$

My question is how can i use a finite differences scheme to integrate this?. I tried using finite differences directly in the logarithm but apparently it is not the best way.

I will be grateful if someone can help me. Thanks.