Asymptotics of oscillatory Riemann–Hilbert problems

A classical method of stationary phase for oscillatory integrals is generalized to oscillatory Riemann–Hilbert problems of the kind arising in the theory of integrable nonlinear equations. The proposed approach is developed for the phase with N first‐order stationary points, and the final formulas can immediately be applied to the problem of long‐time behavior of the solutions of equations such as the NLS, KdV, mKdV sine‐Gordon, and others.