Riemann-Hilbert approach and double-pole solutions for the third-order flow equation of DNLS-type equation with nonzero boundary conditions

In this paper, the Riemann-Hilbert approach is applied to study a third-order flow equation of derivative nonlinear Schrödinger-type equation with nonzero boundary conditions. By utilizing the analytical, symmetric, and asymptotic properties of eigenfunctions, a generalized Riemann-Hilbert problem i...

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Bibliographic Details
Published in:Physica scripta 2024-06, Vol.99 (6), p.65238
Main Authors: Qin, Yue, Huang, Ye-Hui, Yao, Yuqin, Zhang, Juan
Format: Article
Language:English
Subjects:
double-pole solutions
nonzero boundary conditions
Riemann–Hilbert approach
single-pole solutions
the third-order flow equation
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Summary:In this paper, the Riemann-Hilbert approach is applied to study a third-order flow equation of derivative nonlinear Schrödinger-type equation with nonzero boundary conditions. By utilizing the analytical, symmetric, and asymptotic properties of eigenfunctions, a generalized Riemann-Hilbert problem is formulated for the third-order flow equation of derivative nonlinear Schrödinger-type equation with nonzero boundary conditions. The formulas of N -soliton solutions for cases of single pole and double poles are given. We present some kinds of soliton solutions of these two cases according to different distributions of spectral parameters to study the dynamical behavior of them.
ISSN:0031-8949
1402-4896
DOI:10.1088/1402-4896/ad468b