Riemann-Hilbert problems for a nonlocal reverse-spacetime Sasa-Satsuma hierarchy of a fifth-order equation and its soliton solutions

TL;DR

This paper formulates a Riemann-Hilbert problem for a nonlocal fifth-order Sasa-Satsuma equation, deriving soliton solutions and analyzing their dynamics based on a nonlocal matrix spectral problem.

Contribution

It introduces a novel nonlocal reverse-spacetime fifth-order Sasa-Satsuma equation and constructs its soliton solutions via a Riemann-Hilbert approach, expanding integrable systems theory.

Findings

Explicit soliton solutions derived from the Riemann-Hilbert problem.

The dynamics of solitons analyzed through explicit formulas.

The formulation of a Riemann-Hilbert problem for a nonlocal integrable equation.

Abstract

We aim to present and analyze a nonlinear nonlocal reverse-spacetime fifth-order scalar Sasa-Satsuma equation, based on a nonlocal $5 \times 5$ matrix AKNS spectral problem. Starting from a nonlocal matrix AKNS spectral problem, local and nonlocal symmetry relations are derived from a group of rotations. A kind of Riemann-Hilbert problem is formulated, which allows to generate soliton solutions by using vectors lying in the kernel of the matrix Jost solutions. When reflection coefficients are zeros, the jump matrix is the identity and the corresponding Riemann-Hilbert problem yields soliton solutions, whose explicit formulas enable us to explore their dynamics.