Derrick’s theorem beyond a potential

Scalar field theories with derivative interactions are known to possess solitonic excitations, but such solitons are generally unsatisfactory because the effective theory fails precisely where nonlinearities responsible for the solitons are important. A new class of theories possessing (internal) galilean invariance can in principle bypass this difficulty. Here, we show that these galileon theories do not possess stable solitonic solutions. As a by-product, we show that no stable solitons exist for a different class of derivatively coupled theories, describing for instance the infrared dynamics of superfluids, fluids, solids and some k-essence models.