Microbreaking and polycnoidal waves in the Ostrovsky-Hunter equation

For the Ostrovsky-Hunter equation, ut+uux=∫xu(x',t)dx', we show that waves of arbitrarily small amplitude can break: u(x,0)=bcos(kx) breaks if b>1/(3k2). However, long waves are nonbreaking, approximated by Stokes' series for N-polycnoidal waves of sufficiently large N. Tiny short wave perturbations on long waves 'microbreak', creating tiny fronts or shocks while the long waves are unaffected