Asymptotic Behavior for a Class of Solutions to the Critical Modified Zakharov-kuznetsov Equation

We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation ut + 6uux + uxxx + uxyy = 0, (x, y) ∈ R, t ∈ R, which is known to have global solution for given data in u(x, y, 0) = u0(x, y) ∈ H(R) satisfying ‖u0‖L2 < √ 3‖φ‖L2 , where φ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5].