We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis main...We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.展开更多
随着故障预测与健康管理(prognostics and health management,PHM)技术的快速发展和实际应用的不断深入,PHM相关标准的建立就显得非常重要。首先给出了PHM的概念和技术内涵,指明PHM标准应该规范的内容,并介绍了国内外的研究现状;其次综...随着故障预测与健康管理(prognostics and health management,PHM)技术的快速发展和实际应用的不断深入,PHM相关标准的建立就显得非常重要。首先给出了PHM的概念和技术内涵,指明PHM标准应该规范的内容,并介绍了国内外的研究现状;其次综述了现有国外标准化组织和机构中与相关的标准,并按照视情维修(CBM),故障预测与健康管理(PHM),综合航天器健康管理(IVHM)和状态使用和管理系统(HUMS)对PHM相关标准进行了深入分析;最后对我国PHM标准开发提出了几点建议,并指明了下一步工作的重点和研究方向。展开更多
基金the Fundamental Research Funds for the Central Universities(Grant No.2024MS126).
文摘We study the dynamics of fundamental and double-pole breathers and solitons for the focusing and defocusing nonlinear Schrodinger equation with the sextic operator under non-zero boundary conditions. Our analysis mainly focuses onthe dynamical properties of simple- and double-pole solutions. Firstly, through verification, we find that solutions undernon-zero boundary conditions can be transformed into solutions under zero boundary conditions, whether in simple-pole ordouble-pole cases. For the focusing case, in the investigation of simple-pole solutions, temporal periodic breather and thespatial-temporal periodic breather are obtained by modulating parameters. Additionally, in the case of multi-pole solitons,we analyze parallel-state solitons, bound-state solitons, and intersecting solitons, providing a brief analysis of their interactions.In the double-pole case, we observe that the two solitons undergo two interactions, resulting in a distinctive “triangle”crest. Furthermore, for the defocusing case, we briefly consider two situations of simple-pole solutions, obtaining one andtwo dark solitons.
文摘随着故障预测与健康管理(prognostics and health management,PHM)技术的快速发展和实际应用的不断深入,PHM相关标准的建立就显得非常重要。首先给出了PHM的概念和技术内涵,指明PHM标准应该规范的内容,并介绍了国内外的研究现状;其次综述了现有国外标准化组织和机构中与相关的标准,并按照视情维修(CBM),故障预测与健康管理(PHM),综合航天器健康管理(IVHM)和状态使用和管理系统(HUMS)对PHM相关标准进行了深入分析;最后对我国PHM标准开发提出了几点建议,并指明了下一步工作的重点和研究方向。
