Date, Etsuro; Kashiwara, Masaki; Jimbo, Michio; Miwa, Tetsuji Transformation groups for soliton equations. (English) Zbl 0571.35098 Nonlinear integrable systems - classical theory and quantum theory, Proc. RIMS Symp., Kyoto 1981, 39-119 (1983). In this paper, the authors make a survey of their papers [M. Kashiwara and T. Miwa [Proc. Japan Acad., Ser. A 57, 342–347 (1981; Zbl 0538.35065), E. Date, M. Kashiwara and T. Miwa, ibid. 57, 387–392 (1981; Zbl 0538.35066); and the following reviews] about the Lie algebras as infinitesimal transformations of solutions for soliton equations. They mainly deal with the Kadomtsev-Petviashvili equations (KP), Korteweg-de Vries equation, and KP hierarchy. Reviewer: Guo Boling (Beijing) Cited in 16 ReviewsCited in 253 Documents MSC: 35Q51 Soliton equations 35Q53 KdV equations (Korteweg-de Vries equations) 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems Keywords:integrability condition; KP hierarchy; Hirota bilinear form; vertex operator; infinitesimal Bäcklund transformation; survey; Kadomtsev-Petviashvili equations; Korteweg-de Vries equation Citations:Zbl 0571.35099; Zbl 0571.35100; Zbl 0571.35101; Zbl 0571.35102; Zbl 0571.35103; Zbl 0571.35104; Zbl 0571.35105; Zbl 0571.35106; Zbl 0538.35065; Zbl 0538.35066 × Cite Format Result Cite Review PDF