Riemann–Hilbert problems and soliton solutions for the reverse space-time nonlocal Sasa–Satsuma equation

• Published in: Nonlinear dynamics Vol. 111; no. 11; pp. 10473 - 10485
• Main Authors: Zhang, Wen-Xin, Liu, Yaqing, Chen, Xin, Zeng, Shijie
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.06.2023; Springer Nature B.V
• Subjects: Asymptotic properties; Automotive Engineering; Boundary conditions; Classical Mechanics; Control; Dynamical Systems; Eigenvalues; Eigenvectors; Engineering; Inverse scattering; Mechanical Engineering; Nonlinear systems; Original Paper; Solitary waves; Spacetime; Symmetry; Vibration; Riemann–Hilbert promblems; Soliton solutions; 37K40; 35Q51; The reverse space-time nonlocal Sasa–Satsuma equation; Symmetry constraints
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-023-08388-9

The main work of this paper is to study the soliton solutions and asymptotic behavior of the integrable reverse space-time nonlocal Sasa–Satsuma equation, which is derived from the coupled two-component Sasa–Satsuma system with a specific constraint. The soliton solutions of the nonlocal Sasa–Satsuma equation are constructed through solving the inverse scattering problems by Riemann–Hilbert method. Compared with local systems, discrete eigenvalues and eigenvectors of the reverse space-time nonlocal Sasa–Satsuma equation have novel symmetries and constraints. On the basis of these symmetry relations of eigenvalues and eigenvectors, the one-soliton and two-soliton solutions are obtained and the dynamic properties of these solitons are shown graphically. Furthermore, the asymptotic behaviors of two-soliton solutions are analyzed. All these results about physical features and mathematical properties may be helpful to comprehend nonlocal nonlinear system better.