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The initial-boundary value problems of the new two-component generalized Sasa–Satsuma equation with a \(4\times 4\) matrix Lax pair

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Abstract

In this paper, we consider a new two-component Sasa–Satsuma equation, which can simulate the propagation and interaction of ultrashort pulses and describe the propagation of femtosecond pulses in optical fibers. The unified transformation method is used to construct a \(4\times 4\) matrix Riemann–Hilbert problem. Then, the solution of the initial-boundary value problems for the new two-component generalized Sasa–Satsuma equation well can be obtained by solving this matrix Riemann–Hilbert problem. In addition, we obtain that the spectral functions satisfy an important global relation.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under the grant 11835011, 12147115 and 11905124, Natural Science Foundation of Anhui Province under the grant 2108085QA09, Project funded by China Postdoctoral Science Foundation under grant 2022M712833, University Natural Science Research Project of Anhui Province under the grant KJ2021A1094.

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Authors and Affiliations

  1. School of Mathematics and Finance, Chuzhou University, Anhui, 239000, China

    Beibei Hu & Ling Zhang

  2. Department of Physics, Zhejiang Normal University, Jinhua, 321004, China

    Beibei Hu & Ji Lin

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  1. Beibei Hu
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Hu, B., Zhang, L. & Lin, J. The initial-boundary value problems of the new two-component generalized Sasa–Satsuma equation with a \(4\times 4\) matrix Lax pair. Anal.Math.Phys. 12, 109 (2022). https://doi.org/10.1007/s13324-022-00716-3

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