Abstract
Global and local existence results for the solutions of systems of stochastic Schrödinger equations with multiplicative noise and quadratic nonlinear terms are discussed in this paper. The same system in the deterministic treatment was studied in [23] where the mass and energy are conserved. In our stochastic situation, those are not conserved.
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Acknowledgements
This work was supported by JSPS KAKENHI No. JP22J00787 (for M.H.), No. JP19H00644 and No. JP20K03671 (for S.M.). The authors would like to thank the referees for their careful reading of the manuscript and helpful suggestions. The authors have followed them. This current paper is a revised version of the original manuscript [22] which was submitted to the arXiv.
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Hamano, M., Hashimoto, S. & Machihara, S. Global and Local Solutions of Stochastic Nonlinear Schrödinger System With Quadratic Interaction. Bull. Iran. Math. Soc. 50, 22 (2024). https://doi.org/10.1007/s41980-024-00863-2
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DOI: https://doi.org/10.1007/s41980-024-00863-2