Geodesic
The Nizhnik–Veselov–Novikov equation with self-consistent sources
Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 1, pp. 130-140 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct the coupled generalization of the Nizhnik–Veselov–Novikov (NVN) equation, i.e., the NVN equation with self-consistent sources (ESCS) and solve it using the so-called source generation procedure. We obtain BKP-type and DKP-type Pfaffian solutions of the NVN ESCS. In addition, we give a bilinear Bäcklund transformation and a Lax pair for the NVN ESCS. Furthermore, this Lax pair can be reduced to a Lax pair for the NVN equation.
Keywords: Nizhnik–Veselov–Novikov equation, self-consistent source, “source generation” procedure, Bäcklund transformation
Mots-clés : Lax pair. 
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Wang Hong-Yan. The Nizhnik–Veselov–Novikov equation with self-consistent sources. Teoretičeskaâ i matematičeskaâ fizika, Tome 157 (2008) no. 1, pp. 130-140. http://geodesic.mathdoc.fr/item/TMF_2008_157_1_a8/

[1] V. K. Mel'nikov, Comm. Math. Phys., 112:4 (1987), 639–652 | DOI | MR | Zbl

[2] V. K. Mel'nikov, Comm. Math. Phys., 126:1 (1989), 201–215 | DOI | MR | Zbl

[3] J. Leon, A. Latifi, J. Phys. A, 23:8 (1990), 1385–1403 | DOI | MR | Zbl

[4] Y. Matsuno, J. Phys. A, 24:6 (1991), L273–L277 | DOI | MR | Zbl

[5] Y. Zeng, W.-X. Ma, R. Lin, J. Math. Phys., 41:8 (2000), 5453–5489 | DOI | MR | Zbl

[6] S.-F. Deng, D.-Y. Chen, D.-J. Zhang, J. Phys. Soc. Japan, 72:9 (2003), 2184–2192 | DOI | MR | Zbl

[7] X.-B. Hu, H.-Y. Wang, Inverse Problems, 22:5 (2006), 1903–1920 | DOI | MR | Zbl

[8] H.-Y. Wang, J. Math. Anal. Appl., 330:2 (2007), 1128–1138 | DOI | MR | Zbl

[9] H.-Y. Wang, J. Hu, H.-W. Tam, J. Phys. A, 40:44 (2007), 13385–13394 | DOI | MR | Zbl

[10] L. P. Nizhnik, DAN SSSR, 254:2 (1980), 332–335 | MR | Zbl

[11] A. P. Veselov, S. P. Novikov, DAN SSSR, 279:1 (1984), 20–24 ; 279:4 (1984), 784–788 ; S. P. Novikov, A. P. Veselov, Phys. D, 18:1–3 (1986), 267–273 | MR | Zbl | MR | Zbl | DOI | MR | Zbl

[12] Y. Tagami, Phys. Lett. A, 141:3–4 (1989), 116–120 | DOI | MR

[13] P. G. Grinevich, R. G. Novikov, DAN SSSR, 286:1 (1986), 19–22 | MR | Zbl

[14] M. Boiti, J. Leon, M. Manna, F. Pempinelli, Inverse Problems, 2:3 (1986), 271–279 | DOI | MR | Zbl

[15] L. V. Bogdanov, TMF, 70:2 (1987), 309–314 | DOI | MR | Zbl

[16] C. Athorne, A. Fordy, J. Math. Phys., 28:9 (1987), 2018–2024 | DOI | MR | Zbl

[17] Y. Cheng, J. Math. Phys., 32:1 (1991), 157–162 | DOI | MR | Zbl

[18] X.-Biao Hu, J. Phys. A, 27:4 (1994), 1331–1338 | DOI | MR | Zbl

[19] S.-Y. Lou, Phys. Lett. A, 277:2 (2000), 94–100 | DOI | MR | Zbl

[20] L. M. Alonso, E. M. Reus, E. O. Moreno, Phys. Lett. A, 159:8–9 (1991), 384–389 | DOI | MR

[21] Y. Ohta, J. Phys. Soc. Japan, 61:11 (1992), 3928–3933 | DOI | MR

[22] M. Jimbo, T. Miwa, Publ. Res. Inst. Math. Sci., 19:3 (1983), 943–1001 | DOI | MR | Zbl

[23] R. Hirota, The Direct Method in Soliton Theory, Cambridge Tracts in Math., 155, eds. A. Nagai, J. Nimmo, C. Gilson, Cambridge University Press, Cambridge, 2004 | MR | Zbl