Waves of maximal height for a class of nonlocal equations with homogeneous symbols

We discuss the existence and regularity of periodic traveling-wave solutions a class nonlocal equations with homogeneous symbol order -r, where r > 1. Based on properties convolution operator, we apply analytic bifurcation theory show that highest, peaked, solution is reached as limiting case at end main curve. The highest wave proved to be exactly Lipschitz. As an application our analysis, reformulate steady reduced Ostrovsky equation in form terms Fourier multiplier operator m(k) = k$^{-2}$. Thereby recover its unique 2π-periodic, peaked solution, having property being Lipschitz crest.