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

Xianguo Geng, Mingming Chen & Kedong Wang

DOI: 10.4208/eajam.220920.250920

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 = {Geng , XianguoChen , Mingming and Wang , Kedong}, 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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