Abstract
We study the asymptotic behavior of oscillatory Riemann–Hilbert problems (RHPs) arising in the Ablowitz-Kaup-Newell-Segur hierarchy of integrable nonlinear partial differential equations. Our method is based on the Deift–Zhou nonlinear steepest descent method in which the given RHP localizes to small neighborhoods of stationary phase points. In their original work, Deift and Zhou only considered analytic phase functions. Subsequently, Varzugin extended the Deift–Zhou method to a certain restricted class of nonanalytic phase functions. In this paper, we extend Varzugin’s method to a substantially more general class of nonanalytic phase functions. In our work, real variable methods play a key role.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
