1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China; 2. School of Mathematical and Statistical Sciences, The University of Texs Rio Grande Valley, Edinburg, TX 78539, USA; 3. MOE International Joint Laboratory of Trustworthy Software, East China Normal University, Shanghai 200062, China; 4. Department of Physics, Zhejiang Normal University, Jinhua 321004, China
Abstract In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlevé 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.
Fund: 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), the Outstanding Doctoral Dissertation Cultivation Plan of Action (Grant No. YB2016039), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things (Grant No. ZF1213). Some work was done during the third author (Chen) visited the University of Texas-Rio Grande Valley (UTRGV). The second author (Qiao) thanks the UTRGV President Endowed Professorship (Grant No. 450000123), and the UTRGV College of Science Seed Grant (Grant No. 240000013) for partial support.
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