Sharp asymptotic behavior of solutions to Benjamin-Ono type equations—short range case

Abstract This paper studies the large time behavior of a small solution to the generalized Benjamin-Ono equation with a short range nonlinearity, i.e., with the power of nonlinearity greater than 3. In this case, it is well-known that the solution is asymptotically free as t → ∞ . We are interested in the asymptotic expansion of the solution, and determine the second asymptotic term. In order to specify the second asymptotic term, we will apply a technique of Fourier series expansion.