In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of th...In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.展开更多
In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduce...In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.展开更多
基金Project supported by the Natural Science Foundation of Zhejiang Province of China (Grant No. LY12A01007)the National Natural Science Foundation of China (Grant Nos. 11201251, 10971109, and 11271210)+1 种基金K. C. Wong Magna Fund in Ningbo Universitythe DST,DAE-BRNS, UGC, and CSIR, Government of India, for the financial support through major projects
文摘In this paper, considering the Hirota and the Maxwell–Bloch （H-MB） equations which are governed by femtosecond pulse propagation through a two-level doped fiber system, we construct the Darboux transformation of this system through a linear eigenvalue problem. Using this Daurboux transformation, we generate multi-soliton, positon, and breather solutions （both bright and dark breathers） of the H-MB equations. Finally, we also construct the rogue wave solutions of the above system.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11675054 and 11435005)+3 种基金the Outstanding Doctoral Dissertation Cultivation Plan of Action(Grant No.YB2016039)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)the UTRGV President Endowed Professorship(Grant No.450000123)the UTRGV College of Science Seed Grant(Grant No.240000013)for partial support
文摘In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.
