Standing wave solution for the generalized Jackiw-Pi model

Abstract

Abstract We study the existence and nonexistence of the standing wave solution for the generalized Jackiw-Pi model by using variational method. Depending on interaction strength λ \lambda , we have three different situations. The existence and nonexistence of the standing wave solution correspond to 1 < λ 1\lt \lambda and 0 < λ < 1 0\lt \lambda \lt 1 , respectively. We have the explicit solution of self-dual equation for the borderline λ = 1 \lambda =1 .