arXiv subjects

Alle Adjiri

Publications and source records attributed to Alle Adjiri.

2 recordsLinked to original sources

arXiv2022

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

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.

nlin.SI↗

arXiv2022

Riemann-Hilbert problems of a non-local reverse-time AKNS system of six-order and dynamical behaviours of $N$-soliton

In this paper, we are going to solve nonlinear nonlocal reverse-time six-component six-order AKNS system. We used reverse-time reduction to reduce the coupled system to an integrable six-order NLS-type equation. Starting from the spectral problem of the AKNS system, a Riemann-Hilbert problem will be formulated. This formulation allows to generate soliton solutions by using the vectors lying in the kernel of the matrix Jost solutions. When reflection coefficients are zeros, the jump matrix is identity and the corresponding Riemann-Hilbert problem yields soliton solutions, leading to explore their dynamics.

nlin.SI↗