2013/10/18 by Marcus Kardell, Kardell, Marcus
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #35D30 #58D19 #76M60 #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #Biological Activity of Diterpenoids and Biflavonoids #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1310.4927
openalex publication_date 2013/10/18 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28
In this article we study a new kind of unbounded solutions to the Novikov\nequation, found via a Lie symmetry analysis. These solutions exhibit peakon\ncreation, i.e., these solutions are smooth up until a certain finite time, at\nwhich a peak is created. We show that the functions are still weak solutions\nfor those times where the peak lives. We also find similar unbounded solutions\nwith peakon creation in the related Camassa-Holm equation, by making an ansatz\ninspired by the Novikov solutions. Finally, we see that the same ansatz for the\nDegasperis-Procesi equation yields unbounded solutions where a peakon is\npresent for all times.\n