Solving Nonlinear PDEs in MATLAB: FDM or FEM Method? | Code Included

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    Matlab Nonlinear Pde
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physgeekgeek
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I have the following equation to solve:

u_{tt}=12{u_x}^2+12u_{xx}+{u_x}^4+6u_{xx}{u_x}^2+4u_{xxx}u_x+3{u_{xx}}^2+u_{xxxx}

I have been told to look into FDM or FEM. My question, is it possible to code something in MATLAB to solve this and if so what is the best method to use and how do I do it? It would also be useful if there is some code already that I can change to fit the problem.

Cheers
 
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I am looking for solution u(x,t) btw