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Article overview
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Rogue waves of the Hirota and the Maxwell-Bloch equations | Chuanzhong Li
; Jingsong He
; K. Porsezian
; | Date: |
6 May 2012 | Abstract: | In this paper, we derive Darboux transformation of the Hirota and the
Maxwell-Bloch(H-MB) equations which is governed by femtosecond pulse
propagation through erbium doped fibre and further generalize it to the matrix
form of the n-fold Darboux transformation of this system. This n-fold Darboux
transformation implies the determinant representation of n-th new solutions of
$(E^{[n]},p^{[n]}, eta^{[n]})$ generated from known solution of $(E, p,eta)$.
The determinant representation of $(E^{[n]},p^{[n]} ,eta^{[n]})$ provides
soliton solutions, positon solutions and breather solutions (both bright and
dark breathers) of the H-MB equations. Particularly we also construct bright
and dark rogue wave solution for the H-MB equations which is one of the hot
topics in mathematics and physics nowadays. | Source: | arXiv, 1205.1191 | Services: | Forum | Review | PDF | Favorites |
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