The Wave Breaking for Whitham-Type Equations Revisited
Jean‐Claude Saut, Yuexun Wang
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 and has been proven independently in (Yang, SIAM J. Math. Anal., 53 (2021), pp. 5756--5802). In all cases we provide simpler proofs than the known ones.
Topics & Concepts
MathematicsBurgers' equationMathematical proofType (biology)Mathematical analysisKorteweg–de Vries equationShock waveBreaking waveHilbert transformWave equationPartial differential equationWave propagationNonlinear systemGeometryPhysicsEcologySpectral densityQuantum mechanicsBiologyThermodynamicsStatisticsAdvanced Mathematical Physics ProblemsNonlinear Waves and SolitonsNonlinear Photonic Systems