Nondispersive solutions to the mass critical half-wave equation in two dimensions

摘要

We consider the half-wave equation with mass critical in two dimensions @@@ {iu(t)=Du-|u|u, @@@ u(t(0),x)=u(0)(x), @@@ First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with ground state mass ||u(0)||(2)=||Q||(2), where Q is the ground state solution of equation DQ+Q=Q(2).

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