期刊
STUDIES IN APPLIED MATHEMATICS
卷 145, 期 1, 页码 97-136出版社
WILEY
DOI: 10.1111/sapm.12313
关键词
Hirota's bilinear method; KP hierarchy reduction method; nonlocal Mel'nikov equation; soliton; semi-rational solution
资金
- National Natural Science Foundation of China [11701382, 11971288]
In this paper, the Hirota's bilinear method and Kadomtsev-Petviashvili hierarchy reduction method are applied to construct soliton, line breather and (semi-)rational solutions to the nonlocal Mel'nikov equation with nonzero boundary conditions. These solutions are expressed as NxN Gram-type determinants. When N is even, soliton, line breather and (semi-)rational solutions on the constant background are derived while these solutions are located on the periodic background for odd N. Regularity of these solutions and their connections with the local Mel'nikov equation are analyzed for proper choices of parameters that appear in the solutions. The dynamics of the solutions are discussed in detail. All possible configurations of soliton and lump solutions are found for N=2,3. Several interesting dynamical behaviors of semi-rational solutions are observed. It is shown that certain lumps may exhibit fusion and fission phenomena during their interactions with solitons while some lump may change its direction of movement after it collides with solitons.
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