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PreprintarXiv licencearXiv

The \texorpdfstring{N-soliton}{N-soliton} solution formula for the Kaup--Kupershmidt equation

  • Tuncay Aktosun
  • Ramazan Ercan
  • Mehmet Unlu
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Abstract

An explicit formula is presented for the N-soliton solution to the Kaup--Kupershmidt equation, for any positive integer N, by using the input data set consisting of N distinct positive pj-values and N arbitrarily chosen positive cj-values. The formula is derived from the solution to the inverse scattering problem for a third-order linear operator in the reflectionless case with the pj-values related to the bound-state poles of a transmission coefficient and the cj-values related to the bound-state dependency constants. It is indicated how the formula is constructed from the solution to a Riemann--Hilbert problem and from the solution to a Marchenko integral equation used in the formulation of the aforementioned inverse scattering problem.

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Cite

BibTeXRIS
BibTeX
@misc{aktosun2026texorpdfstringnsolitonnsoliton,
  title = {{The \texorpdfstring$\mathbf N$-solitonN-soliton solution formula for the Kaup--Kupershmidt equation}},
  author = {Tuncay Aktosun and Ramazan Ercan and Mehmet Unlu},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.05613},
  eprint = {2611.05613},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.05613},
}
RIS
TY  - UNPB
TI  - The \texorpdfstring{N-soliton}{N-soliton} solution formula for the Kaup--Kupershmidt equation
AU  - Tuncay Aktosun
AU  - Ramazan Ercan
AU  - Mehmet Unlu
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2611.05613
UR  - https://arxiv.org/abs/2611.05613
AB  - An explicit formula is presented for the N-soliton solution to the Kaup--Kupershmidt equation, for any positive integer N, by using the input data set consisting of N distinct positive p_j-values and N arbitrarily chosen positive c_j-values. The formula is derived from the solution to the inverse scattering problem for a third-order linear operator in the reflectionless case with the p_j-values related to the bound-state poles of a transmission coefficient and the c_j-values related to the bound-state dependency constants. It is indicated how the formula is constructed from the solution to a Riemann--Hilbert problem and from the solution to a Marchenko integral equation used in the formulation of the aforementioned inverse scattering problem.
ER  -