East Asian J. Appl. Math., 11 (2021), pp. 181-206.
Published online: 2020-11
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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} }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.