Higher order asymptotics of the modified non-linear schrödinger equation

Higher Order Asymptotics of the Modified Non-Linear Schrödinger Equation

Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution systems which take the form of Lax-pair isospectral deformations, the higher order asymptotics as t→±∞ (x/t∼O(1)) of the solution to the Cauchy problem for the modified non-linear Schrödinger equation, i∂tu+ 1 2 ∂ x u+ |u|u+is∂x(|u|u) = 0, s ∈ R>0, which is a model for non-linear pulse propagation in optical fibres...

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

Using the matrix Riemann-Hilbert (RH) factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method (ISM), we obtain, in the solitonless sector, the leading order asymptotics as t → ±∞ of the solution to the Cauchy initial-value problem for the modified non-linear Schrödinger equation (MNLSE), i∂tu + 1 2 ∂ xu + |u|2u + is∂x(|u|u) = 0,...

Higher Order Unitary Integrators for the Schrödinger Equation

on the effect of linear & non-linear texts on students comprehension and recalling

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Periodic waves of a discrete higher order nonlinear Schrödinger equation ∗

The Hirota equation is a higher order extension of the nonlinear Schrödinger equation by incorporating third order dispersion and one form of self steepening effect. New periodic waves for the discrete Hirota equation are given in terms of elliptic functions. The continuum limit converges to the analogous result for the continuous Hirota equation, while the long wave limit of these discrete per...