Analytic-bilinear approach to integrable hierarchies. 1. Generalized KP hierarchy

被引:23
作者
Bogdanov, LV [1 ]
Konopelchenko, BG
机构
[1] Univ Lecce, Dipartimento Fis, Consortium EINSTEIN, I-73100 Lecce, Italy
[2] Sez INFN, I-73100 Lecce, Italy
[3] LD Landau Theoret Phys Inst, Moscow 117940, Russia
关键词
D O I
10.1063/1.532540
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
An analytic-bilinear approach for construction and study of integrable hierarchies, in particular, the KP hierarchy is proposed. It starts with the generalized Hirota identity for the Cauchy-Baker-Akhiezer (CBA) function and leads to a generalized KP hierarchy in the form of compact functional equations containing a special shift operator. A generalized KP hierarchy incorporates the basic KP hierarchy, modified KP hierarchy, KP singularity manifold equation hierarchy, and corresponding hierarchies of linear problems. Different "vertical" levels of the generalized KP hierarchy are connected via invariants of the Combescure symmetry group. The resolution of functional equations also gives rise to the tau function and the addition formulas for it. (C) 1998 American Institute of Physics.
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页码:4683 / 4700
页数:18
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