15 research outputs found
Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector
Using the matrix Riemann-Hilbert factorisation approach for non-linear
evolution equations (NLEEs) integrable in the sense of the inverse scattering
method, we obtain, in the solitonless sector, the leading-order asymptotics as
tends to plus and minus infinity of the solution to the Cauchy
initial-value problem for the modified non-linear Schrodinger equation: also
obtained are analogous results for two gauge-equivalent NLEEs; in particular,
the derivative non-linear Schrodinger equation.Comment: 29 pages, 5 figures, LaTeX, revised version of the original
submission, to be published in Inverse Problem