Volume 11, Issue 1
Application of the Nonlinear Steepest Descent Method to the Coupled Sasa-Satsuma Equation

Xianguo Geng, Mingming Chen & Kedong Wang

East Asian J. Appl. Math., 11 (2021), pp. 181-206.

Published online: 2020-11

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  • Abstract

We use spectral analysis to reduce Cauchy problem for the coupled Sasa-Satsuma equation to a 5 × 5 matrix Riemann-Hilbert problem. The upper and lower triangular factorisations of the jump matrix and a decomposition of the vector-valued spectral function are given. Applying various transformations related to the Riemann-Hilbert problems and suitable decompositions of the jump contours and the nonlinear steepest descent method, we establish the long-time asymptotics of the problem.

  • Keywords

Coupled Sasa-Satsuma equation, nonlinear steepest descent method, long-time asymptotics.

  • AMS Subject Headings

35Q53, 35B40, 35Q55

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-11-181, author = {Xianguo and Geng and and 9669 and and Xianguo Geng and Mingming and Chen and and 9670 and and Mingming Chen and Kedong and Wang and and 9671 and and Kedong Wang}, title = {Application of the Nonlinear Steepest Descent Method to the Coupled Sasa-Satsuma Equation}, journal = {East Asian Journal on Applied Mathematics}, year = {2020}, volume = {11}, number = {1}, pages = {181--206}, abstract = {

We use spectral analysis to reduce Cauchy problem for the coupled Sasa-Satsuma equation to a 5 × 5 matrix Riemann-Hilbert problem. The upper and lower triangular factorisations of the jump matrix and a decomposition of the vector-valued spectral function are given. Applying various transformations related to the Riemann-Hilbert problems and suitable decompositions of the jump contours and the nonlinear steepest descent method, we establish the long-time asymptotics of the problem.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.220920.250920}, url = {http://global-sci.org/intro/article_detail/eajam/18419.html} }
TY - JOUR T1 - Application of the Nonlinear Steepest Descent Method to the Coupled Sasa-Satsuma Equation AU - Geng , Xianguo AU - Chen , Mingming AU - Wang , Kedong JO - East Asian Journal on Applied Mathematics VL - 1 SP - 181 EP - 206 PY - 2020 DA - 2020/11 SN - 11 DO - http://doi.org/10.4208/eajam.220920.250920 UR - https://global-sci.org/intro/article_detail/eajam/18419.html KW - Coupled Sasa-Satsuma equation, nonlinear steepest descent method, long-time asymptotics. AB -

We use spectral analysis to reduce Cauchy problem for the coupled Sasa-Satsuma equation to a 5 × 5 matrix Riemann-Hilbert problem. The upper and lower triangular factorisations of the jump matrix and a decomposition of the vector-valued spectral function are given. Applying various transformations related to the Riemann-Hilbert problems and suitable decompositions of the jump contours and the nonlinear steepest descent method, we establish the long-time asymptotics of the problem.

Xianguo Geng, Mingming Chen & Kedong Wang. (2020). Application of the Nonlinear Steepest Descent Method to the Coupled Sasa-Satsuma Equation. East Asian Journal on Applied Mathematics. 11 (1). 181-206. doi:10.4208/eajam.220920.250920
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