Sasa-Satsuma type matrix integrable hierarchies and their Riemann-Hilbert problems and soliton solutions. (English) Zbl 1512.37081
Summary: Sasa-Satsuma type matrix integrable hierarchies are generated from taking two group reductions of replacing the spectral parameter with its complex conjugate and its negative in the matrix AKNS spectral problems. Based on the Lax pairs and the adjoint lax pairs, Riemann-Hilbert problems and thus inverse scattering transforms are formulated for the resulting Sasa-Satsuma type matrix integrable hierarchies, and their soliton solutions are generated from the associated reflectionless Riemann-Hilbert problems.
MSC:
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 37K15 | Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems |
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 35Q15 | Riemann-Hilbert problems in context of PDEs |
| 35Q51 | Soliton equations |
Keywords:
matrix spectral problem; group reduction; integrable hierarchy; Riemann-Hilbert problem; inverse scattering transform; soliton solutionReferences:
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