Novel solitons and higher-order solitons for the nonlocal generalized Sasa-Satsuma equation of reverse-space-time type

The general soliton solutions and higher-order soliton solutions for the nonlocal generalized Sasa-Satsuma (SS) equation of reverse-space-time type are explored. Firstly, a novel nonlocal generalized SS equation is derived, and the infinitely many conserved quantities and conservation laws are considered. Secondly, some novel symmetry properties and nonlocal constraints for eigenvalues, eigenvectors and scattering data are obtained, which is quite different from the local ones. Then, in the framework of the Riemann-Hilbert problem and by the special nonlocal properties, the N-soliton formula with determinant and the higher-order soliton formulas are constructed for the nonlocal generalized SS equation by a limit technique. Thirdly, some new patterns and unusual dynamical behaviors of the N-soliton and the higher-order soliton solutions for the nonlocal generalized SS equation are exhibited and explored. The general single soliton is always collapsing periodically whether the eigenvalues are pure imaginary or not, but when the absolute value of the eigenvalue approaches to zero, the solution tends to be a standing solution, which does not move with time. Besides, some novel interesting physical patterns for the two-soliton solution are obtained, such as a singular wave in the periodical background and two-soliton solution with two singular branches. It is worth mentioning that the two-soliton solution does not degenerate into a bounded breathing soliton instead of a breathing singular wave when lambda(2) = -lambda(1)*. And the higher-order soliton with one double zero is singular and collapsing periodically while the soliton with triple zero is nonsingular when the eigenvalue is purely imaginary. query Please check the edit made in the article title.

Automated summary

The general soliton solutions and higher-order soliton solutions for the nonlocal generalized Sasa-Satsuma (SS) equation are explored. The study derived a novel nonlocal generalized SS equation, considered conservation laws, and obtained symmetry properties and nonlocal constraints. The N-soliton formula and higher-order soliton formulas were constructed using the Riemann-Hilbert problem and nonlocal properties. The study also exhibited and explored new patterns and unusual dynamical behaviors of the soliton solutions.