Riemann–Hilbert approach and N-soliton solutions for a new two-component Sasa–Satsuma equation

A new two-component Sasa–Satsuma equation associated with a 4×4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times 4$$\end{document} matrix spectral problem is proposed by resorting to the zero-curvature equation. Riemann–Hilbert problems are formulated on the basis of spectral analysis of the 4×4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\times 4$$\end{document} matrix Lax pair for the two-component Sasa–Satsuma equation, from which zero structures of the Riemann–Hilbert problems are investigated. As applications, N-soliton formulas of the two-component Sasa–Satsuma equation are obtained by solving a particular Riemann–Hilbert problem corresponding to the reflectionless case. Further, the obtained N-soliton formulas are expressed by the ratios of determinants, which are more compact and convenient for symbolic computations. Moreover, the interaction dynamics of the multi-soliton solutions are analyzed and graphically illustrated.