The wave breaking for Whitham-type equations revisited
Jean-Claude Saut, Yuexun Wang
TL;DR
This paper proves wave breaking phenomena for various Whitham-type equations, including some not previously analyzed, and offers simplified proofs for known cases, advancing understanding of shock formation in these models.
Contribution
It establishes wave breaking results for the Burgers-Hilbert and other Whitham-type equations, with new proofs and extensions of previous work.
Findings
Wave breaking is proven for the Burgers-Hilbert equation.
Simpler proofs are provided for classical Whitham and fractional KdV equations.
The results contribute to the theoretical understanding of shock formation in nonlinear wave models.
Abstract
We prove wave breaking (shock formation) for some Whitham-type equations which include the Burgers-Hilbert equation, the fractional Korteweg-de Vries equation, and the classical Whitham equation. The result seems to be new for the Burgers-Hilbert equation. In the other cases we provide simpler proofs than the known ones.
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