Mass-concentration of low-regularity blow-up solutions to the focusing 2D modified Zakharov–Kuznetsov equation

We consider the focusing modified Zakharov–Kuznetsov (mZK) equation in two space dimensions. prove that solutions which blow up finite time \(H^1(\mathbb {R}^{2})\) norm have property they concentrate a non-trivial portion of their mass (more precisely, at least amount equal to ground state) blow-up time. For finite-time \(H^s(\mathbb {R}^2)\) for \(\frac{17}{18}< s < 1\), we slightly weaker result. Moreover, stronger concentration result can be extended range \( \frac{17}{18} \le 1\) under an additional assumption on upper bound rate solution. The main tools used here are I-method and profile decomposition theorem bounded family functions.