Abstract
Under investigation in this paper is the AB system, which describes marginally unstable baroclinic wave packets in geophysical fluids. Through symbolic computation, Lax pair and conservation laws are derived and the Darboux transformation is constructed for this system. Furthermore, three types of breathers on the continuous wave (cw) background are generated via the obtained Darboux transformation. The following contents are mainly discussed by figures plotted: (1) Modulation instability processes of the Akhmediev breathers in the presence of small perturbations; (2) Propagations characteristics of Ma solitons; (3) Dynamic features of the breathers evolving periodically along the straight line with a certain angle of z-axis and t-axis.
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Acknowledgements
We express our sincere thanks to each member of our discussion group for their suggestions. This work has been supported by Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi under Grant No. 2013110, by the National Natural Science Foundation of China under Grant No. 61250011 and by the Natural Science Foundation of Shanxi Province under Grant No. 2012011004-3.
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Guo, R., Hao, HQ. & Zhang, LL. Dynamic behaviors of the breather solutions for the AB system in fluid mechanics. Nonlinear Dyn 74, 701–709 (2013). https://doi.org/10.1007/s11071-013-0998-1
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DOI: https://doi.org/10.1007/s11071-013-0998-1