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Inverse Scattering Transform for the Generalized Derivative Nonlinear Schrödinger Equation via Matrix Riemann–Hilbert Problem

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  • Fang Fang
  • Beibei Hu
  • Ling Zhang
  • Abdullahi Yusuf

Abstract

The inverse scattering transformation for a generalized derivative nonlinear Schrödinger (GDNLS) equation is studied via the Riemann–Hilbert approach. In the direct scattering process, we perform the spectral analysis of the Lax pair associated with a 2×2 matrix spectral problem for the GDNLS equation. Then, the corresponding Riemann–Hilbert problem is constructed. In the inverse scattering process, we obtain an N-soliton solution formula for the GDNLS equation by solving the Riemann–Hilbert problem with the reflection-less case. In addition, we express the N-soliton solution of the GDNLS equation as determinant expression.

Suggested Citation

  • Fang Fang & Beibei Hu & Ling Zhang & Abdullahi Yusuf, 2022. "Inverse Scattering Transform for the Generalized Derivative Nonlinear Schrödinger Equation via Matrix Riemann–Hilbert Problem," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-9, April.
    • Handle: RePEc:hin:jnlmpe:3967328
    DOI: 10.1155/2022/3967328
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