New solutions with peakon creation in the Camassa-Holm and Novikov equations
2015 (English)In: Journal of Nonlinear Mathematical Physics, ISSN 1402-9251, Vol. 22, no 1Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
Taylor and Francis: STM, Behavioural Science and Public Health Titles , 2015. Vol. 22, no 1
Novikov; Camassa-Holm; peakon; weak solution; 76M60; 58D19; 35D30
IdentifiersURN: urn:nbn:se:liu:diva-113491DOI: 10.1080/14029251.2015.996435ISI: 000346180500001OAI: oai:DiVA.org:liu-113491DiVA: diva2:781959