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

摘要

We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation u(t) + 6u(2)u(x) + u(xxx) + u(xyy) = 0, (x, y) is an element of R-2, t is an element of R, which is known to have global solution for given data in u(x, y, 0) = u(0)(x, y) is an element of H-1(R-2) satisfying parallel to u(0)parallel to(L2) < root 3 parallel to phi parallel to(L2), where phi 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. [1, 2].