Soliton solutions and a bi-Hamiltonian structure of the fifth-order nonlocal reverse-spacetime Sasa-Satsuma-type hierarchy via the Riemann-Hilbert approach

Our objective is to explore the intricacies of a nonlinear nonlocal fifth-order scalar Sasa-Satsuma equation in reverse spacetime which is rooted in a nonlocal $ 5 \times 5 $ matrix AKNS spectral problem. Starting with this spectral problem, we derive both local and nonlocal symmetry relations throu...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 9; pp. 23234 - 23267
Main Authors Ahmed, Ahmed M. G., Adjiri, Alle, Manukure, Solomon
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
mkdv equation
nonlocal reverse-spacetime
riemann-hilbert problem
sasa-satsuma hierarchy
soliton dynamics
soliton solutions
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Summary:Our objective is to explore the intricacies of a nonlinear nonlocal fifth-order scalar Sasa-Satsuma equation in reverse spacetime which is rooted in a nonlocal $ 5 \times 5 $ matrix AKNS spectral problem. Starting with this spectral problem, we derive both local and nonlocal symmetry relations through rotations within a defined group. We then formulate a specific type of Riemann-Hilbert problem, facilitating the generation of soliton solutions. These solutions are generated by utilizing vectors that reside in the kernel of the matrix Jost solutions. Under the condition where reflection coefficients are null, the jump matrix reduces to the identity, leading to soliton solutions via the corresponding Riemann-Hilbert problem. The explicit formulas of these soliton solutions enable a comprehensive exploration of their dynamics.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.20241130