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Experimental evidence of bouncing localized structures in a nonlinear optical system is reported. Oscillations in the position of the localized states are described by a consistent amplitude equation, which we call the Lifshitz normal form equation, in analogy with phase transitions. Localized structures are shown to arise close to the Lifshtiz point, where… (More)

For any pattern α of length at most two, we enumerate equivalence classes of Motzkin paths where two paths of the same length are equivalent whenever they coincide on all occurrences of the pattern α.

- B S Nahapetian, A N Petrossian
- 2009

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