Annals of Mathematical Sciences and Applications
Volume 2 (2017)
Guest Editors: Tai-Chia Lin (National Taiwan University), Wen-Wei Lin (National Chiao Tung University), Tony Wen-Hann Sheu (National Taiwan University), Weichung Wang (National Taiwan University), Chih-wen Weng (National Chiao Tung University), and Salil Vadhan (Harvard University).
Planar unimodular Baker-Akhiezer function for the nonlinear Schrödinger equation
Pages: 343 – 384
We present the construction of the planar Baker–Akhiezer (BA) function for the nonlinear Schrödinger equation (NLS), corresponding to the finite-genus solutions of the NLS equation. The BA function is described as the unimodular solution of a matrix Riemann–Hilbert problem in the complex plane with piecewise constant jumps across a set of arcs.
Riemann–Hilbert problems, the nonlinear Schrödinger equation, the Baker–Akhiezer function, finite-genus solutions
2010 Mathematics Subject Classification
Primary 35Q55, 37K10. Secondary 30E20, 30E25, 35B10, 35B15.
Paper received on 7 June 2016.