Abstract

The so-called KdV6 equation has, since its discovery, been the subject of much interest. In this paper we present a matrix version of this equation. On the one hand, we use the Darboux transformation to derive its Bäcklund transformation and a nonlinear superposition formula. These are then used, in the case of upper-triangular matrices, to obtain one- and two-soliton solutions. We find that wave components can combine to produce rogue waves. On the other hand, we derive a second matrix partial differential equation, for which we give auto-Bäcklund transformations of a different kind, similar to those usually given for Painlevé equations.

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Elsevier

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URI

https://hdl.handle.net/10115/204297

DOI

https://doi.org/https://doi.org/10.1016/j.cnsns.2025.108605

Date

2025-01-12

Description

We gratefully acknowledge the following financial support: Project PID2020-115273GB-I00 and Grant RED2022-134301-T funded by MCIN/AEI/10.13039/501100011033. The authors also gratefully acknowledge financial support from the Universidad Rey Juan Carlos as members of the Grupo de investigación de alto rendimiento DELFO.

Keywords

Matriz KdV6 , Rogue waves , Bäcklund transformations , Multisoliton solutions

Citation

Gordoa, P. R., Pickering, A., & Wattis, J. A. D. (2025). On a matrix KdV6 equation. Communications in Nonlinear Science and Numerical Simulation, 143, 108605. https://doi.org/10.1016/j.cnsns.2025.108605

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