Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation

12/30/2020 ∙ by C. Klein, et al. ∙ 0

We present a detailed numerical study of solutions to the Zakharov-Kuznetsov equation in three spatial dimensions. The equation is a three-dimensional generalization of the Korteweg-de Vries equation, though, not completely integrable. This equation is L^2-subcritical, and thus, solutions exist globally, for example, in the H^1 energy space. We first study stability of solitons with various perturbations in sizes and symmetry, and show asymptotic stability and formation of radiation, confirming the asymptotic stability result in <cit.> for a larger class of initial data. We then investigate the solution behavior for different localizations and rates of decay including exponential and algebraic decays, and give positive confirmation toward the soliton resolution conjecture in this equation. Finally, we investigate soliton interactions in various settings and show that there is both a quasi-elastic interaction and a strong interaction when two solitons merge into one, in all cases always emitting radiation in the conic-type region of the negative x-direction.



There are no comments yet.


page 10

page 13

page 15

page 17

page 19

page 23

page 25

page 27

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.