Physical Sciences and Mathematics Commons^™

Long-Time Asymptotics For Mkdv Type Reduced Equations Of The Akns Hierarchy In Weighted L2 Sobolev Spaces, Fudong Wang

USF Tampa Graduate Theses and Dissertations

The long-time asymptotics of nonlinear integrable partial differential equations is one of the important research areas in the field of integrable systems. The main tool to analyze the long-time behaviors is the so-called nonlinear steepest descent method, or Deift-Zhou's method, which was born in 1993. To apply Deift-Zhou's method, one first uses the inverse scattering transform to formulate the nonlinear PDEs in terms of an oscillatory 2 by 2 matrix Riemann-Hilbert problem (RHP). After about 15 years of development, a generalized version of Deift-Zhou's method, the ∂—steepest method, came out. The ∂—steepest descent method is a useful method for analyzing …