| 1. |
- Euler, Marianna, 1961-, et al.
(författare)
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Multipotentializations and nonlocal symmetries: Kupershmidt, Kaup-Kupershmidt and Sawada-Kotera equations
- 2017
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 24:3, s. 303-314
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- In this letter we report a new invariant for the Sawada-Kotera equation that is obtained by a systematic potentialization of the Kupershmidt equation. We show that this result can be derived from nonlocal symmetriesand that, conversely, a previously known invariant of the Kaup-Kupershmidt equation can be recovered using potentializations.
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| 2. |
- Euler, Norbert, 1964-, et al.
(författare)
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Local and Nonlocal Symmetries in Mathematical Physics
- 2017
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Taylor & Francis. - 1402-9251 .- 1776-0852. ; 24:Suppl. 1, s. 1-2
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 3. |
- Kardell, Marcus
(författare)
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New solutions with peakon creation in the Camassa-Holm and Novikov equations
- 2015
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Ingår i: Journal of Nonlinear Mathematical Physics. - : Taylor and Francis: STM, Behavioural Science and Public Health Titles. - 1402-9251 .- 1776-0852. ; 22:1
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Tidskriftsartikel (refereegranskat)abstract
- In this article we study a new kind of unbounded solutions to the Novikov equation, found via a Lie symmetry analysis. These solutions exhibit peakon creation, i.e., these solutions are smooth up until a certain finite time, at which a peak is created. We show that the functions are still weak solutions for those times where the peak lives. We also find similar unbounded solutions with peakon creation in the related Camassa-Holm equation, by making an ansatz inspired by the Novikov solutions. Finally, we see that the same ansatz for the Degasperis-Procesi equation yields unbounded solutions where a peakon is present for all times.
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