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Nonlocal symmetries for bilinear equations and their applications

胡星标 研究员(中国科学院)
Friday, July 3rd, 2020, 3:00 PM  腾讯会议(会议 ID:338 873 259)
*主持人:傅蔚 副教授
*时间: 2020 年7月3日 15:00-16:00
*地点: 腾讯会议(会议 ID:338 873 259)

In this talk, nonlocal symmetries for the bilinear KP and bilinear BKP equations are restudied. Two arbitrary parameters are introduced in these nonlocal symmetries by considering gauge invariance of the bilinear KP and bilinear BKP equations under a certain transformation. By expanding these nonlocal symmetries in power series of each of two parameters, we have derived two types of bilinear NKP hierarchies and two types of bilinear NBKP hierarchies. An impressive observation is that bilinear positive and negative KP (NKP) and BKP hierarchies may be derived from the same nonlocal symmetries for the KP and BKP equations. Besides, as two concrete examples, we have derived bilinear B?cklund transformations for t_2?flow of the NKP hierarchy and t_{-1}?flow of the NBKP hierarchy. All these results have made it clear that more beautiful integrability properties would be found for these obtained NKP hierarchies and NBKP hierarchies. Because KP and BKP hierarchies have played an essential role in soliton theory, we believe that the bilinear NKP and NBKP hierarchies will have their right place in this field.

胡星标,中国科学院数学与系统科学研究院研究员,博导。主要研究方向为可积系统与数值算法。现任《应用数学学报》英文版编委,《数学进展》编委,《Journal of Nonlinear Math. Phys.》编委,《Pacific Journal of Appl. Math.》编委。
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