Unconditional uniqueness for the periodic modified Benjamin–Ono equation by normal form approach

Abstract We show that the solution (in sense of distribution) to Cauchy problem with periodic boundary condition associated modified Benjamin–Ono equation is unique in $L^\infty _t(H^s(\mathbb{T} ))$ for $s>1/2$. The proof based on analysis a normal form obtained by infinitely many reduction steps using integration parts time after suitable gauge transform.