期刊
PHYSICAL REVIEW E
卷 85, 期 5, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevE.85.056607
关键词
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资金
- National Natural Science Foundation of China [11075055, 11175092, 61021004, 10735030]
- National High Technology Research and Development Program [2011AA010101]
- Shanghai Leading Academic Discipline Project [B412]
- Shanghai Natural Science Foundation [11ZR1411200]
- Ningbo University
In nonlinear science, it is very difficult to find exact interaction solutions among solitons and other kinds of complicated waves such as cnoidal waves and Painleve waves. Actually, even if for the most well-known prototypical models such as the Kortewet-de Vries (KdV) equation and the Kadomtsev-Petviashvili (KP) equation, this kind of problem has not yet been solved. In this paper, the explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetries which are related to Darboux transformation for the well-known KdV equation. The same approach also yields some other types of interaction solutions among different types of solutions such as solitary waves, rational solutions, Bessel function solutions, and/or general Painleve II solutions.
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