Soliton stability and resolution conjectures for the 3D Zakharov–Kuznetsov equation

Let the 3D Zakharov–Kuznetsov equation be given by, and let the soliton solutions be those defined by --. A perturbation is understood to be of soliton-like initial data, and sufficiently localized and smooth initial data are considered for the resolution claim. Soliton stability and resolution conjectures. The soliton solutions are orbitally and asymptotically stable, with stability holding on a large set of perturbations of soliton-like initial data. Moreover, solutions with sufficiently localized and smooth initial data decompose into solitons and radiation as $t\to\infty$; equivalently, the soliton resolution conjecture holds for the 3D Zakharov–Kuznetsov equation. The paper investigates these claims numerically through the stability of solitons, soliton resolution, radiation, and soliton interactions in this non-integrable three-dimensional model; the supplied text does not establish their general mathematical resolution.