| Abstract: |
| We consider the stability for line solitary waves of the two dimensional Zakharov--Kuznetsov equation on cylindrical spaces which is one of a high dimensional generalization of Korteweg--de Vries equation.The orbital and asymptotic stability of the one soliton of Korteweg--de Vries equation on the energy space was proved by Benjamin, Pego--Weinstein and Martel--Merle. We regard the one soliton of Korteweg--de Vries equation as a line solitary wave of Zakharov--Kuznetsov equation on cylindrical spaces. In this talk, we talk about the orbital and asymptotic stability and the transverse instability of the line solitary waves of Zakharov--Kuznetsov equation. |
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