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An integrable matrix NLS equation on star graph and symmetry-dependent connection conditions of vertex

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Abstract

An integrable matrix nonlinear Schrödinger (NLS) equation on a star graph with semi-infinite incoming and outgoing bonds are presented by attaching a matrix NLS equation to each bond. We demonstrate that the matrix NLS equation on star graphs has infinitely many constants of motion and is a completely integrable system by establishing a link between the solutions of the matrix NLS equation on each bond and those of the standard matrix NLS equation on a line. On star graphs, novel symmetry-dependent connection conditions of the vertex for the matrix NLS equations are put forth.

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Acknowledgements

The authors would like to express our sincere gratitude to the anonymous referees for their corrections and valuable comments. This work was supported by the National Natural Science Foundation of China (Grant No. 12171209) and Graduate Research and Innovation Projects of Jiangsu Province (Grant No. KYCX20-2205).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu, 221116, People’s Republic of China

    Ruguang Zhou & Hongyang Zhu

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  1. Ruguang Zhou
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  2. Hongyang Zhu
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Correspondence to Ruguang Zhou.

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Zhou, R., Zhu, H. An integrable matrix NLS equation on star graph and symmetry-dependent connection conditions of vertex. Comp. Appl. Math. 42, 69 (2023). https://doi.org/10.1007/s40314-023-02201-4

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