Abstract
The Riemann–Hilbert problem and soliton solutions to the high-order nonlinear Schrödinger equation with matrix version is studied with an equivalent spectral problem. Moreover, a pair of Jost solutions \({\mathcal {J}}^{\pm }\), satisfied the asymptotic conditions \({\mathcal {J}}^{\pm }\rightarrow {\mathcal {I}}\) and matrix spectral problem, can be used to obtain the matrix Riemann–Hilbert problem. This work makes the crucial use of the inverse scattering for the studied equation. In the case of reflection-less, based on the two type of zero structures of \(\det (P^{+})\), the different soliton solutions are theoretically and graphically presented.
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Acknowledgements
We are grateful to the reviewers for their encouraging suggestions that were helpful in improving this paper further.
Funding
This work is supported by the National Natural Science Foundation of China under Grant (Nos. 11971133, 12101159).
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Chen, Y., Yan, XW. Inverse scattering and soliton solutions of high-order matrix nonlinear Schrödinger equation. Nonlinear Dyn 108, 4057–4067 (2022). https://doi.org/10.1007/s11071-022-07363-0
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DOI: https://doi.org/10.1007/s11071-022-07363-0
Keywords
- High-order matrix nonlinear Schrödinger equation
- Inverse scattering transform
- Riemann–Hilbert problem
- Soliton solution