In 3+1 dimensions with signature +1 -1 -1 -1,
L=12∂μϕ∂μϕ−ϕ2/2−ϕ4/4
field equation: ◻ϕ+ϕ+ϕ3=0
(check this)
◻=∂2t−∇2
Note that it is not a Mexican hat. I guess this haven't been solved exactly before but, somebody have shown or discarded that there could be soliton solutions or at least solitary waves?
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