On exponential decay properties of solutions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation

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Abstract

We study here the special decay properties of real solutions to the initial value problem associated with the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation. More precisely, we prove the properties of exponential decay of order 3/2 above the plane x + y + z = 0 as time evolves. This property is related with the persistence properties of the solution flow in weighted Sobolev spaces and sharp unique continuation properties of solutions to this problem.

Keywords

(3 + 1)-dimensional modified Zakharov-Kuznetsov equation / exponential decay / energy estimate

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