Riemann-Hilbert Approach and N-soliton Solutions of the Sasa-Satsuma Equation with Higher-Order Terms

Abstract This paper focuses on solving the Sasa-Satsuma equation with higher-order terms using the Riemann-Hilbert (RH) method. Firstly, we derive the Lax pairs related to the matrix spectral problem of the equation. Secondly, we perform spectral analysis on the Lax pairs of the equation, thereby constructing a RH problem for the equation. Under the condition of the reflectionless case, we solve for the \(N\)-soliton solutions of the equation and use symbolic computation in Maple to illustrate the graphical forms of the single-soliton and double-soliton solutions.