Geodesic
Bilinear equations for the strict KP hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 512-526 Cet article a éte moissonné depuis la source Math-Net.Ru

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We describe two modules for the algebra $P\!sd$ of pseudodifferential operators; for each of them, we define an associated system from which the Lax equations of the strict KP hierarchy can be obtained as compatibility conditions. We construct a set of bilinear equations on these modules that characterizes solutions of the strict KP hierarchy that are obtained by dressing the basic generator of $P\!sd$.
Keywords: integrable deformation, pseudodifferential operator, strict KP hierarchy, dual wave function, bilinear form.
Mots-clés : compatible Lax equation 
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G. F. Helminck; E. A. Panasenko; S. V. Polenkova. Bilinear equations for the strict KP hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 185 (2015) no. 3, pp. 512-526. http://geodesic.mathdoc.fr/item/TMF_2015_185_3_a7/

[1] R. Hirota, “Direct method of finding exact solutions of nonlinear evolution equations”, Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications, Lecture Notes in Mathematics, 515, ed. R. M. Miura, 1976, 40–68 | DOI | MR | Zbl

[2] M. Sato, Y. Mori, RIMS Kokyuroku, 388 (1980), 183; M. Sato, Y. Sato, RIMS Kokyuroku, 414 (1981), 181

[3] E. Date, M. Jimbo, M. Kashiwara, T. Miwa, “Transformation groups for soliton equations”, Nonlinear Integrable Systems – Classical Theory and Quantum Theory (Kyoto, Japan, 13–16 May, 1981), eds. M. Jimbo, T. Miwa, World Sci., Singapore, 1983, 39–119 | MR | Zbl

[4] V. Kats, Beskonechnomernye algebry Li, Mir, M., 1993 | MR

[5] G. F. Khelmink, A. G. Khelmink, E. A. Panasenko, TMF, 174:1 (2013), 154–176 | DOI | DOI | MR | Zbl

[6] G. F. Helminck, A. G. Helminck, E. A. Panasenko, J. Geom. Phys., 85 (2014), 196–205 | DOI | MR | Zbl

[7] G. F. Helminck, G. F. Post, Lett. Math. Phys., 16:4 (1988), 359–364 | DOI | MR | Zbl

[8] G. Segal, G. Wilson, Publ. Math. Inst. Hautes Étud. Sci., 61 (1985), 5–65 | DOI | MR | Zbl