Scattering theory For Quadratic Nonlinear Schrödinger System in dimension six

2021/07/12 by Chuanwei Gao, Fanfei Meng, Gao, Chuanwei +5 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2107.05299

openalex publication_date 2021/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the solutions to the energy-critical quadratic nonlinear Schrödinger system in H¹× H¹, where the sign of its potential energy can not be determined directly. If the initial data \rm u₀ is radial or non-radial but satisfies the mass-resonance condition, and its energy is below that of the ground state, using the compactness/rigidity method, we give a complete classification of scattering versus blowing-up dichotomies depending on whether the kinetic energy of \rm u₀ is below or above that of the ground state.

Cited by

• Dynamics of the Energy-Critical Nonlinear Schrödinger System in \mathbb R⁴
• The focusing energy-critical nonlinear Schrödinger system with power-type growth nonlinearities in the radial case

Related

• On the energy-critical quadratic nonlinear Schrödinger system with three waves
• Scattering for quadratic-type Schr "odinger systems in dimension five\n without mass-resonance
• Scattering for the quadratic nonlinear Schrödinger system in ℝ⁵ without mass-resonance condition
• A sharp scattering threshold level for mass-subcritical nonlinear Schrödinger system
• Threshold solutions for the energy-critical NLS system with quadratic interaction