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arXiv · 2611.05613

The \texorpdfstring{$\mathbf N$-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 $\mathbf N$-soliton solution to the Kaup--Kupershmidt equation, for any positive integer $\mathbf N,$ by using the input data set consisting of $\mathbf N$ distinct positive $p_j$-values and $\mathbf N$ 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.

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Tuncay Aktosun, Ramazan Ercan, Mehmet Unlu. 2026-11-03. The \texorpdfstring{$\mathbf N$-soliton}{N-soliton} solution formula for the Kaup--Kupershmidt equation. https://arxiv.org/abs/2611.05613

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