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Licensed Unlicensed Requires Authentication Published by De Gruyter December 16, 2017

Initial-Boundary Value Problems for the Coupled Higher-Order Nonlinear Schrödinger Equations on the Half-line

  • Bei-bei Hu , Tie-cheng Xia EMAIL logo , Ning Zhang and Jin-bo Wang

Abstract

In this article, we use the unified transform method to analyze the initial-boundary value problem for the coupled higher-order nonlinear Schrödinger equations on the half-line. Suppose that the solution {q1(x,t),q2(x,t)} exists, we show that it can be expressed in terms of the unique solution of a matrix Riemann–Hilbert problem formulated in the plane of the complex spectral parameter λ.

MSC 2010: 35G31; 35Q15; 35Q51

Funding statement: The work was partially supported by the National Natural Science Foundation of China under Grant nos. 11271008, 61072147, 11601055.

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Received: 2017-4-6
Accepted: 2017-10-29
Published Online: 2017-12-16
Published in Print: 2018-2-23

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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