Volume 11, Issue 1
The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation

Xin-Mei Zhou, Shou-Fu Tian, Jin-Jie Yang & Jin-Jin Mao

East Asian J. Appl. Math., 11 (2021), pp. 143-163.

Published online: 2020-11

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  • Abstract

A four-component nonlinear Schrödinger equation associated with a 5×5 Lax pair is investigated. A spectral problem is analysed and the Jost functions are used in order to derive a Riemann-Hilbert problem connected with the equation under consideration. $N$-soliton solutions of the equation are obtained by solving the Riemann-Hilbert problem without reflection. For $N = 1$ and $N = 2$, the local structure and dynamic behavior of some special solutions are analysed by invoking their graphic representations.

  • Keywords

Four-component nonlinear Schrödinger equation, Riemann-Hilbert approach, $N$-soliton solutions.

  • AMS Subject Headings

35Q51, 35Q53, 35C99, 68W30, 74J35

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-143, author = {Xin-Mei and Zhou and and 9664 and and Xin-Mei Zhou and Shou-Fu and Tian and and 9665 and and Shou-Fu Tian and Jin-Jie and Yang and and 9666 and and Jin-Jie Yang and Jin-Jin and Mao and and 9667 and and Jin-Jin Mao}, title = {The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {11}, number = {1}, pages = {143--163}, abstract = {

A four-component nonlinear Schrödinger equation associated with a 5×5 Lax pair is investigated. A spectral problem is analysed and the Jost functions are used in order to derive a Riemann-Hilbert problem connected with the equation under consideration. $N$-soliton solutions of the equation are obtained by solving the Riemann-Hilbert problem without reflection. For $N = 1$ and $N = 2$, the local structure and dynamic behavior of some special solutions are analysed by invoking their graphic representations.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.100620.170920}, url = {http://global-sci.org/intro/article_detail/eajam/18417.html} }
TY - JOUR T1 - The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation AU - Zhou , Xin-Mei AU - Tian , Shou-Fu AU - Yang , Jin-Jie AU - Mao , Jin-Jin JO - East Asian Journal on Applied Mathematics VL - 1 SP - 143 EP - 163 PY - 2020 DA - 2020/11 SN - 11 DO - http://doi.org/10.4208/eajam.100620.170920 UR - https://global-sci.org/intro/article_detail/eajam/18417.html KW - Four-component nonlinear Schrödinger equation, Riemann-Hilbert approach, $N$-soliton solutions. AB -

A four-component nonlinear Schrödinger equation associated with a 5×5 Lax pair is investigated. A spectral problem is analysed and the Jost functions are used in order to derive a Riemann-Hilbert problem connected with the equation under consideration. $N$-soliton solutions of the equation are obtained by solving the Riemann-Hilbert problem without reflection. For $N = 1$ and $N = 2$, the local structure and dynamic behavior of some special solutions are analysed by invoking their graphic representations.

Xin-Mei Zhou, Shou-Fu Tian, Jin-Jie Yang & Jin-Jin Mao. (2020). The Riemann-Hilbert Approach and $N$-Soliton Solutions of a Four-Component Nonlinear Schrödinger Equation. East Asian Journal on Applied Mathematics. 11 (1). 143-163. doi:10.4208/eajam.100620.170920
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