Controllable rogue waves in coupled nonlinear Schrödinger equations with varying potentials and nonlinearities

Exact rogue wave solutions, including the first-order rogue wave solutions and the second-order ones, are constructed for the system of two coupled nonlinear Schrödinger (NLS) equations with varying potentials and nonlinearities. The method employed in this paper is the similarity transformation, which allows us to map the inhomogeneous coupled NLS equations with variable coefficients into the integrable Manakov system, whose explicit solutions have been well studied before. The result shows that the rogue wavelike solutions obtained by this transformation are controllable. Concretely, we illustrate how to control the trajectories of wave centers and the evolutions of wave peaks, and analyze the dynamic behaviors of the rogue wavelike solutions.