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The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line

The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line
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Year:    2018

East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 531–548

Abstract

An integrable coherently coupled nonlinear Schrödinger system describing the propagation of polarised optical waves in an isotropic medium with a generalized 4 × 4 matrix Ablowitz-Kaup-Newell-Segur-type Lax pair is studied. The corresponding initial-boundary value problem is reduced to a matrix Riemann-Hilbert problem in the complex plane. Moreover, it is shown that the associated spectral functions depend on each other and satisfy a global relationship.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.080318.240418

East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 3 : pp. 531–548

Published online:    2018-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    18

Keywords:    Riemann-Hilbert problem coherently coupled nonlinear Schrödinger system initial-boundary value problem unified transform method.

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