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Some results for a system of NLS arising in optical materials with χ3 nonlinear response
  • Yingxin Duan,
  • Guoqing Zhang
Yingxin Duan
University of Shanghai for Science and Technology

Corresponding Author:yingxin_d@163.com

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Guoqing Zhang
University of Shanghai for Science and Technology
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Abstract

In this paper, we investigate the nonlinear Schödinger equations with cubic interactions, arising in nonlinear optics. To begin, we prove the existence results for normalized ground state solutions in the L 2 -subcritical case and L 2 -supercritical case respectively. Our proofs relies on the Concentration-compactness principle, Pohozaev manifold and rearrangement technique. Then, we establish the nonexistence of normalized ground state solutions in the L 2 -critical case by finding that there exists a threshold. In addition, based on the existence of the normalized solutions, we also establish the blow-up results are shown by using localized virial estimates, and a new blow-up criterion which is related to normalized solutions.
24 Dec 2022Submitted to Mathematical Methods in the Applied Sciences
24 Dec 2022Submission Checks Completed
24 Dec 2022Assigned to Editor
03 Jan 2023Review(s) Completed, Editorial Evaluation Pending
16 Jan 2023Reviewer(s) Assigned
18 Apr 2023Editorial Decision: Revise Minor
25 Apr 20231st Revision Received
26 Apr 2023Submission Checks Completed
26 Apr 2023Assigned to Editor
26 Apr 2023Review(s) Completed, Editorial Evaluation Pending
05 May 2023Reviewer(s) Assigned
25 Jun 2023Editorial Decision: Accept