Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector

Details Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector

1996-12-27

arxiv.org/abs/solv-int/9701001v2

Nonlinear Sciences

Pattern Formation and Solitons

29 pages, 5 figures, LaTeX, revised version of the original submission, to be published in Inverse Problems

Scientific paper

10.1088/0266-5611/13/5/014

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 $t$ 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.

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