Wave Breaking in the Periodic Integrable Hunter-Saxton Equation with a Dispersive Term

摘要

Considered here is the periodic Cauchy problem for an integrable Hunter-Saxton equation with a dispersive term.Firstly,we derive a precise blow-up criterion of strong solutions to the equation.Secondly,sufficient conditions guaranteeing the development of breaking waves in finite time are demonstrated by applying some conservative quantities and the nethod of characteristics,respectively.Finally,the exact blow-up rate is determined.