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Volume 8, Issue 3
The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line

Beibei Hu, Tiecheng Xia & Wen-Xiu Ma

DOI: 10.4208/eajam.080318.240418

East Asian J. Appl. Math., 8 (2018), pp. 531-548.

Published online: 2018-08

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  • 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.

  • Keywords

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

  • AMS Subject Headings

35G31, 35Q51, 35Q15

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-531, author = {Beibei Hu, Tiecheng Xia and Wen-Xiu Ma}, title = {The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line }, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {3}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080318.240418}, url = {http://global-sci.org/intro/article_detail/eajam/12624.html} }
TY - JOUR T1 - The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line AU - Beibei Hu, Tiecheng Xia & Wen-Xiu Ma JO - East Asian Journal on Applied Mathematics VL - 3 SP - 531 EP - 548 PY - 2018 DA - 2018/08 SN - 8 DO - http://doi.org/10.4208/eajam.080318.240418 UR - https://global-sci.org/intro/article_detail/eajam/12624.html KW - Riemann-Hilbert problem, coherently coupled nonlinear Schrödinger system, initial-boundary value problem, unified transform method. AB -

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.

Beibei Hu, Tiecheng Xia and Wen-Xiu Ma. (2018). The Riemann-Hilbert Approach to Initial-Boundary Value Problems for Integrable Coherently Coupled Nonlinear Schrödinger Systems on the Half-Line . East Asian Journal on Applied Mathematics. 8 (3). 531-548. doi:10.4208/eajam.080318.240418
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