Remarks on the Schrödinger-Lohe model

Hyungjin Huh; Hyungjin Huh

doi:10.3934/nhm.2019030

Networks and Heterogeneous Media

2019, Volume 14, Issue 4: 759-769. doi: 10.3934/nhm.2019030

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Remarks on the Schrödinger-Lohe model

Hyungjin Huh ^,

Department of Mathematics, Chung-Ang University, Seoul 156-756, Republic of Korea

Received: 01 October 2018 Revised: 01 July 2019
82C10, 34E10, 35C05

We study the Schrödinger-Lohe model. Making use of the principal fundamental matrix $ Y $ of linear ODEs with variable coefficients, the coupled nonlinear Schrödinger-Lohe system is transformed into the decoupled linear Schrödinger equations. The boundedness of $ Y $ is shown for the case of complete synchronization. We also study the cases where the principal fundamental matrices can be derived explicitly.
- Schrödinger-Lohe model,
- principal fundamental matrix,
- explicit solution
Citation: Hyungjin Huh. Remarks on the Schrödinger-Lohe model[J]. Networks and Heterogeneous Media, 2019, 14(4): 759-769. doi: 10.3934/nhm.2019030

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Abstract

We study the Schrödinger-Lohe model. Making use of the principal fundamental matrix $ Y $ of linear ODEs with variable coefficients, the coupled nonlinear Schrödinger-Lohe system is transformed into the decoupled linear Schrödinger equations. The boundedness of $ Y $ is shown for the case of complete synchronization. We also study the cases where the principal fundamental matrices can be derived explicitly.

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