期刊
ROYAL SOCIETY OPEN SCIENCE
卷 8, 期 4, 页码 -出版社
ROYAL SOC
DOI: 10.1098/rsos.201910
关键词
y-non-local Mel'nikov equation; Kadomtsev-Petviashvili hierarchy reduction method; bilinear method; soliton solutions; (semi-)rational solutions
资金
- National Natural Science Foundation of China [11701382, 11971288]
- Guangdong Basic and Applied Basic Research Foundation [2021A1515010054]
In this study, general soliton and (semi-)rational solutions to the y-non-local Mel'nikov equation with non-zero boundary conditions are obtained using the Kadomtsev-Petviashvili (KP) hierarchy reduction method. The solutions are expressed in N x N Gram-type determinants with an arbitrary positive integer N. It is found that there are two families of constraints among the parameters appearing in the solutions, leading to different behaviors in generating solitons and lumps.
General soliton and (semi-)rational solutions to the y-non-local Mel'nikov equation with non-zero boundary conditions are derived by the Kadomtsev-Petviashvili (KP) hierarchy reduction method. The solutions are expressed in N x N Gram-type determinants with an arbitrary positive integer N. A possible new feature of our results compared to previous studies of non-local equations using the KP reduction method is that there are two families of constraints among the parameters appearing in the solutions, which display significant discrepancies. For even N, one of them only generates pairs of solitons or lumps while the other one can give rise to odd numbers of solitons or lumps; the interactions between lumps and solitons are always inelastic for one family whereas the other family may lead to semi-rational solutions with elastic collisions between lumps and solitons. These differences are illustrated by a thorough study of the solution dynamics for N = 1, 2, 3. Besides, regularities of solutions are discussed under proper choices of parameters.
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