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

We present a detailed numerical study of solutions to the Zakharov–Kuznetsov equation in three spatial dimensions. The is three-dimensional generalization Korteweg–de Vries equation, though, not completely integrable. This L2-subcritical, and thus, exist globally, for example, H1 energy space. first stability solitons with various perturbations sizes symmetry, show asymptotic formation radiation, confirming result Farah et al. (0000) larger class initial data. then investigate solution behavior different localizations rates decay including exponential algebraic decays, give positive confirmation toward soliton resolution conjecture this equation. Finally, we interactions settings that there are both quasi-elastic interaction strong when two merge into one, all cases always emitting radiation conic-type region negative x-direction.