Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation

Abstract: Resorting to the spectral analysis of the 4 × 4 matrix spectral problem, we construct a 4 × 4 matrix Riemann–Hilbert problem to solve the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation. The nonlinear steepest decent method is extended to study the 4 × 4 matrix Riemann–Hilbert problem, from which the various Deift–Zhou contour deformations and the motivation behind them are given. Through some proper transformations between the corresponding Riemann–Hilbert problems, the basic Riemann–Hilbert problem is reduced to a model Riemann–Hilbert problem, by which the long-time asymptotic behavior to the solution of the initial value problem for the Hermitian symmetric space derivative nonlinear Schrödinger equation is obtained with the help of the asymptotic expansion of the parabolic cylinder function and strict error estimates.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Long-time asymptotic behavior for the Hermitian symmetric space derivative nonlinear Schrödinger equation ; volume:24 ; number:4 ; year:2024 ; pages:819-856 ; extent:38 ; Advanced nonlinear studies ; 24, Heft 4 (2024), 819-856 (gesamt 38)

Contributors, Places and Time

• Creator: Chen, Mingming ; Geng, Xianguo ; Liu, Huan

Further information

• DOI: 10.1515/ans-2023-0145
• URN: urn:nbn:de:101:1-2410041543167.461671700798
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 15.08.2025, 7:38 AM CEST