English

Threshold solutions for the energy-critical NLS system with quadratic interaction

Analysis of PDEs 2025-05-07 v1

Abstract

In this paper, we study the Cauchy problem for a quadratic nonlinear Schr\"{o}dinger system in dimension six. In~\cite{GaoMengXuZheng}, the authors classified the behavior of solutions under the energy constraint E(u)<E(Q)E(u) < E(Q), where QQ denotes the ground state. In this work, we classify the dynamics of radial solutions at the threshold energy E(u)=E(Q)E(u) = E(Q).

Keywords

Cite

@article{arxiv.2505.03124,
  title  = {Threshold solutions for the energy-critical NLS system with quadratic interaction},
  author = {Alex H. Ardila and Liliana Cely and Fanfei Meng},
  journal= {arXiv preprint arXiv:2505.03124},
  year   = {2025}
}

Comments

36 pages, comments are welcome!

R2 v1 2026-06-28T23:22:20.263Z