Existence of periodic travelling wave solutions for a regularized Benjamin–Ono system

In this paper, we discuss the existence of periodic travelling wave solutions of a regularized Benjamin–Ono system by using the topological-degree theory of positive operators on Banach spaces. Furthermore, we use a high-accuracy pseudospectral solver based on a Fourier decomposition to construct numerical approximations of these stationary solutions. The numerical simulations are in perfect agreement with the theoretical results.