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Y. Liu, D. Pelinovsky and A. Sakovich

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Wave breaking in the Ostrovsky-Hunter equation

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SIAM Journal of Mathematical Analysis 42, 1967–1985 (2010)

**Abstract:**

The Ostrovsky–Hunter equation governs evolution of shallow water waves on a rotating
fluid in the limit of small high-frequency dispersion. Sufficient conditions for the
wave breaking in the Ostrovsky–Hunter equation are found both on an infinite line and
in a periodic domain. Using the method of characteristics, we also specify the blow-up
rate at which the waves break. Numerical illustrations of the finite-time wave breaking
are given in a periodic domain.

**Keywords:**

Ostrovsky-Hunter equation, wave breaking,
well-posedness, conserved quantities, method of characteristics.