1997/01/31 by A. V. Kitaev, A. H. Vartanian · 2 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Gauge (firearms) #Infinity #Initial value problem #Integrable system #Inverse #Inverse problem #Inverse scattering problem #Inverse scattering transform #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Schrödinger equation #Nonlinear Waves and Solitons #Numerical methods for differential equations #Order (exchange) #Riemann–Hilbert problem #Schrödinger equation #nlin.PS #nlin.SI #patt-sol #physics.plasm-ph #solv-int
paper · pdf · doi:10.1088/0266-5611/13/5/014
29 pages, 5 figures, LaTeX, revised version of the original submission, to be published in Inverse Problems
arxiv created 1997/06/24 · openalex publication_date 1997/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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, .