Annals of Mathematical Sciences and Applications

Volume 2 (2017)

Number 2

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

DOI: http://dx.doi.org/10.4310/AMSA.2017.v2.n2.a6

Authors

Vladimir Kotlyarov (B. Verkin Institute for Low Temperature Physics, Kharkiv, Ukraine)

Dmitry Shepelsky (B. Verkin Institute for Low Temperature Physics, Kharkiv, Ukraine; and V. Karazin Kharkiv National University, Kharkiv, Ukraine)

Abstract

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.

Keywords

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.

Full Text (PDF format)

Received 7 June 2016

Published 10 August 2017