Numerical Study of Zakharov–Kuznetsov Equations in Two Dimensions

We present a detailed numerical study of solutions to the (generalized) Zakharov–Kuznetsov equation in two spatial dimensions with various power nonlinearities. In $$L^{2}$$ -subcritical case, evidence is presented for stability solitons and soliton resolution generic initial data. $$L^2$$ -critical supercritical cases, appear be unstable against both dispersion blow-up. It conjectured that blow-up happens finite time have some resemblance being self-similar, i.e., core forms rightward moving self-similar type rescaled profile happening at infinity critical case location case. appears similar one generalized Korteweg–de Vries dynamically soliton.