期刊
NONLINEAR DYNAMICS
卷 92, 期 4, 页码 2049-2059出版社
SPRINGER
DOI: 10.1007/s11071-018-4180-7
关键词
Mel'nikov equation; Semi-rational solutions; KP hierarchy reduction method; Lump; Dark soliton
资金
- National Key Research and Development Program of China [2016YFC1402000, 2016YFC1402304]
- NSFC-Shandong Joint Fund for Marine Science Research Centers [U1606405]
Herein, we employ the bilinear method and the KP hierarchy reduction technique for obtaining a hierarchy of semi-rational solutions to the Mel'nikov equation. These semi-rational solutions are given in terms of determinants whose matrix elements have plain algebraic expressions. Under suitable parametric conditions, these semi-rational solutions reduce to rational solutions of the Mel'nikov equation. These semi-rational solutions reveal two opposite types of excitation phenomena: fusion and fission, which are determined by a input parameter gamma. The fundamental (first-order) semi-rational solutions describe a process of a lump originating from a dark soliton and then coexisting with the dark soliton as t >> 0, or a process of a lump coexisting with the dark soliton as t << 0 and then fusing into the dark soliton. The higher-order semi-rational solutions exhibi n(i) (n(i) >= 2) lumps splitting from or annihilating into one dark soliton. The multi-semi-rational solutions describe N (N >= 2) lumps fissuring from or fusing into N-dark solitons.
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