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I've got an action which needs minimising

[tex]\int dr \ r \sqrt{U'^{2}+U^{4}}[/tex]

Where U(r). Simply plugging this into the EL equations yields a nasty looking 2nd order nonlinear differential equation. I'm just wondering if there's an easier way of solving for U(r). I've tried passing over into Hamiltonian mechanics but that seemed to confuse matters slightly (I probably got it wrong). Wondering if there's some implementation of Noether's Theorem that could give a solvable differential equation. As always, much thanks for your help.

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# Minimising the action for surface area in AdS

**Physics Forums | Science Articles, Homework Help, Discussion**