Journal
JOURNAL OF NONLINEAR SCIENCE
Volume 31, Issue 2, Pages -Publisher
SPRINGER
DOI: 10.1007/s00332-021-09680-x
Keywords
Zakharov-Kuznetsov equation; Solitons; Stability; Blow-up dynamics
Categories
Funding
- ANR-FWF Project [ANuI-ANR-17-CE40-0035]
- isite BFC project NAANoD
- EIPHI [ANR-17-EURE-0002]
- European Union Horizon 2020 research and innovation program under the Marie Sklodowska-Curie RISE 2017 Grant [778010]
- NSF [DMS-1815873/1927258]
Ask authors/readers for more resources
A detailed numerical study was conducted on solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities, revealing the stability and soliton resolution for different cases. It was found that solitons exhibit different stability and blow-up characteristics under different conditions.
We present a detailed numerical study of solutions to the (generalized) Zakharov-Kuznetsov equation in two spatial dimensions with various power nonlinearities. In the L-2-subcritical case, numerical evidence is presented for the stability of solitons and the soliton resolution for generic initial data. In the L-2-critical and supercritical cases, solitons appear to be unstable against both dispersion and blow-up. It is conjectured that blow-up happens in finite time and that blow-up solutions have some resemblance of being self-similar, i.e., the blow-up core forms a rightward moving self-similar type rescaled profile with the blow-up happening at infinity in the critical case and at a finite location in the supercritical case. In the L-2-critical case, the blow-up appears to be similar to the one in the L-2-critical generalized Korteweg-de Vries equation with the profile being a dynamically rescaled soliton.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available