Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector

Using the matrix Riemann - Hilbert factorization approach for nonlinear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the leading-order asymptotics as of the solution to the Cauchy initial-value problem for the modified nonlinear Schrödinger equation, , : also obtained are analogous results for two gauge-equivalent NLEEs; in particular, the derivative nonlinear Schrödinger equation, .