期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 327, 期 -, 页码 13-29出版社
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physd.2016.03.012
关键词
Complex short pulse equation; Darboux transformation; Bright soliton; Breather soliton; Rogue wave; Asymptotic analysis
资金
- National Natural Science Foundation of China [11401221, 11271254, 11428102]
- Fundamental Research Funds for the Central Universities [2014ZB0034]
- Ministry of Economy and Competitiveness of Spain [MTM2012-37070]
In the present paper, we are concerned with the general analytic solutions to the complex short pulse (CSP) equation including soliton, breather and rogue wave solutions. With the aid of a generalized Darboux transformation, we construct the N-bright soliton solution in a compact determinant form, the N-breather solution including the Akhmediev breather and a general higher order rogue wave solution. The first and second order rogue wave solutions are given explicitly and analyzed. The asymptotic analysis is performed rigorously for both the N-soliton and the N-breather solutions. All three forms of the analytical solutions admit either smoothed-, cusped- or looped-type ones for the CSP equation depending on the parameters. It is noted that, due to the reciprocal (hodograph) transformation, the rogue wave solution to the CSP equation can be a smoothed, cusponed or a looped one, which is different from the rogue wave solution found so far. Published by Elsevier B.V.
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