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

Abstract

We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we prove the existence of a family of traveling solitary waves. We then show the existence of finite-time blowup solutions with minimal mass $\Vert u_0{\Vert }_2=\Vert Q{\Vert }_2$, where $Q$ is the ground state solution of equation $DQ+Q=Q^2$.

References in corpus (6)

• Uniqueness and Nondegeneracy of Ground States for $(-\Delta {)}^{s}Q+Q-Q^{\alpha +1}=0$ in $\mathbb{R}$
• Boson Stars as Solitary Waves
• Numerical study of fractional Nonlinear Schrödinger equations
• Effective Dynamics for Boson Stars
• On Traveling Solitary Waves and Absence of Small Data Scattering for Nonlinear Half-Wave Equations
• Traveling waves for the quartic focusing Half Wave equation in one space dimension

Cited by in corpus (1)

• Blowup dynamics for Mass Critical Half-wave equation in 3D