Affiliation:
1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People's Republic of China
2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
Abstract
The general coupled Hirota equations are investigated, which describe the wave propagations of two ultrashort optical fields in a fibre. Firstly, we study the modulational instability for the focusing, defocusing and mixed cases. Secondly, we present a unified formula of high-order rational rogue waves (RWs) for the focusing, defocusing and mixed cases, and find that the distribution patterns for novel vector rational RWs of focusing case are more abundant than ones in the scalar model. Thirdly, the
N
th-order vector semirational RWs can demonstrate the coexistence of
N
th-order vector rational RWs and
N
breathers. Fourthly, we derive the multi-dark-dark solitons for the defocsuing and mixed cases. Finally, we derive a formula for the coexistence of dark solitons and RWs. These results further enrich and deepen the understanding of localized wave excitations and applications in vector nonlinear wave systems.
Subject
General Physics and Astronomy,General Engineering,General Mathematics
Cited by
37 articles.
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