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 radiatio...
We consider a model that describes electromigration in nanoconductors known as surface (SEM) equation. Our purpose here is to establish local well-posedness for the associated initial value problem Sobolev spaces from two different points of view. In first one, we study pure Cauchy and $H^s(\mathbb{R}^2)$, $s>1/2$. second on background Korteweg-de Vries solitary traveling wave less regular spac...
