Geodesic
Quasideterminant solutions of the extended noncommutative Kadomtsev–Petviashvili hierarchy
Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 51-69 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a nonauto-Darboux transformation for the extended noncommutative Kadomtsev–Petviashvili (ncKP) hierarchy and consequently derive its quasi-Wronskian solution. We also obtain the quasi-Wronskian solution of the ncKP equation with self-consistent sources (ncKPESCS) as a by-product. Finally, we use the direct verification method to prove the quasi-Wronskian solution of the ncKPESCS.
Keywords: extended noncommutative KP hierarchy, quasi-Wronskian solution, direct verification.
Mots-clés : Darboux transformation 
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Hongxia Wu; Jingxin Liu; Chunxia Li. Quasideterminant solutions of the extended noncommutative Kadomtsev–Petviashvili hierarchy. Teoretičeskaâ i matematičeskaâ fizika, Tome 192 (2017) no. 1, pp. 51-69. http://geodesic.mathdoc.fr/item/TMF_2017_192_1_a3/

[1] M. Hamanaka, Noncommutative solitons and $D$-branes, arXiv: hep-th/0303256

[2] L. D. Paniak, Exact noncommutative KP and KdV multi-solitons, arXiv: hep-th/0105185

[3] M. Hamanaka, “Notes on exact multi-soliton solutions of noncommutative integrable systems”, JHEP, 02 (2007), 094, 17 pp. | DOI | MR

[4] N. Wang, M. Wadati, “Exact multi-line soliton solutions of noncommutative KP equation”, J. Phys. Soc. Japan, 72:8 (2003), 1881–1888 | DOI | MR | Zbl

[5] B. Kupershmidt, KP or mKP. Noncommutative mathematics of Lagrangian, Hamiltonian, and Integrable Systems, AMS, Providence, RI, 2000 | DOI | MR

[6] Z. Zheng, J. S. He, Y. Cheng, “Bäcklund transformation of the noncommutative Gelfand–Dickey hierarchy”, JHEP, 02 (2004), 069, 11 pp. | DOI | MR

[7] M. Hamanaka, “Commuting flows and conservation laws for noncommutative Lax hierarchies”, J. Math. Phys., 46:5 (2005), 052701, 13 pp. | DOI | MR | Zbl

[8] J. S. He, J. Y. Tu, X. D. Li, L. H. Wang, “Explicit flow equations and recursive operator of the ncKP hierarchy”, Nonlinearity, 24:10 (2011), 2875–2890 | DOI | MR | Zbl

[9] M. Hamanaka, “On reductions of noncommutative anti-self-dual Yang–Mills equations”, Phys. Lett. B, 625:3–4 (2003), 324–332 | DOI | MR

[10] P. Etingof, I. Gelfand, V. Retakh, “Factorization of differential operators, quasideterminants, and nonabelian Toda field equations”, Math. Res. Lett., 4:3 (1997), 413–425 | DOI | MR

[11] A. V. Razumov, M. V. Saveliev, “Maximally non-abelian Toda systems”, Nucl. Phys. B, 494:3 (1997), 657–686 | DOI | MR | Zbl

[12] C. R. Gilson, J. J. C. Nimmo, “On a direct approach to quasideterminant solutions of a noncommutative KP equation”, J. Phys. A: Math. Theor., 40:14 (2007), 3839–3850 | DOI | MR | Zbl

[13] C. R. Gilson, J. J. C. Nimmo, C. M. Sooman, “On a direct approach to quasideterminant solutions of a noncommutative modified KP equation”, J. Phys. A: Math. Theor., 41:8 (2008), 085202, 10 pp. | DOI | MR | Zbl

[14] K. R. Gilson, D. K. Nimmo, K. M. Suman, “Matrichnye resheniya nekommutativnogo uravneniya KP i nekommutativnogo uravneniya mKP”, TMF, 159:3 (2009), 448–458 | DOI | DOI | MR | Zbl

[15] C. R. Gilson, S. R. Macfarlane, “Dromion solutions of noncommutative Davey–Stewartson equations”, J. Phys. A: Math. Theor., 42:23 (2009), 235202, 20 pp. | DOI | MR | Zbl

[16] C. X. Li, J. J. C. Nimmo, “Darboux transformations for a twist derivation and quasideterminant solutions to the super KdV equation”, Proc. Roy. Soc. London Ser. A, 466:2120 (2009), 2471–2493 | DOI | MR

[17] C. X. Li, J. J. L. Nimmo, K. M. Tamizhmani, “On solutions to the non-Abelian Hirota–Miwa equation and its continuum limits”, Proc. Roy. Soc. London Ser. A, 465:2105 (2008), 1441–1451 | DOI

[18] X.-M. Zhu, D.-J. Zhang, C.-X. Li, “Quasideterminant solutions of a noncommutative nonisospectral Kadomtsev–Petviashvili equation”, Commun. Theor. Phys., 55:5 (2011), 753–759 | DOI | MR | Zbl

[19] W.-X. Ma, “An extended noncommutative KP hierarchy”, J. Math. Phys., 51:7 (2010), 073505, 19 pp. | DOI | MR | Zbl

[20] I. Gelfand, S. Gelfand, V. Retakh, R. L. Wilson, “Quasideterminants”, Adv. Math., 193:1 (2005), 56–141 | DOI | MR | Zbl

[21] W. Oevel, W. Schief, Applications of Analytic and Geometric Methods to Nonlinear Differential Equations (Exeter, UK, July 14–19, 1992), NATO ASI Series C: Mathematical and Physical Sciences, 413, ed. P. A. Clarkson, Kluwer, Dordrecht, 1993 | MR