The Kadomtsev–Petviashvili equation with self-consistent sources in nonuniform media
Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 181-199 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We derive the nonisospectral Kadomtsev–Petviashvili equation with self-consistent sources and obtain $N$-soliton solutions of the equation by both Hirota's method and the Wronskian technique. We discuss one-soliton characteristics, two-soliton scattering in nonuniform media, and source effects.
Keywords: nonisospectral Kadomtsev–Petviashvili equation with self-consistent sources, Hirota's method, dynamical characteristic, soliton resonance.
Mots-clés : Wronskian technique
@article{TMF_2009_158_2_a1,
     author = {Hao Hong-hai and Zhang Da-jun and Deng Shu-fang},
     title = {The {Kadomtsev{\textendash}Petviashvili} equation with self-consistent sources in~nonuniform media},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {181--199},
     year = {2009},
     volume = {158},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a1/}
}
TY  - JOUR
AU  - Hao Hong-hai
AU  - Zhang Da-jun
AU  - Deng Shu-fang
TI  - The Kadomtsev–Petviashvili equation with self-consistent sources in nonuniform media
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2009
SP  - 181
EP  - 199
VL  - 158
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a1/
LA  - ru
ID  - TMF_2009_158_2_a1
ER  - 
%0 Journal Article
%A Hao Hong-hai
%A Zhang Da-jun
%A Deng Shu-fang
%T The Kadomtsev–Petviashvili equation with self-consistent sources in nonuniform media
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2009
%P 181-199
%V 158
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a1/
%G ru
%F TMF_2009_158_2_a1
Hao Hong-hai; Zhang Da-jun; Deng Shu-fang. The Kadomtsev–Petviashvili equation with self-consistent sources in nonuniform media. Teoretičeskaâ i matematičeskaâ fizika, Tome 158 (2009) no. 2, pp. 181-199. http://geodesic.mathdoc.fr/item/TMF_2009_158_2_a1/

[1] V. K. Mel'nikov, Phys. Lett. A, 133:9 (1988), 493–496 | DOI | MR

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

[3] V. K. Mel'nikov, Inverse Problems, 8:1 (1992), 133–147 | DOI | MR | Zbl

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

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

[6] Y. B. Zeng, W. X. Ma, Y. J. Shao, J. Math. Phys., 42:5 (2001), 2113–2128 | DOI | MR | Zbl

[7] H. H. Chen, C. S. Liu, Phys. Rev. Lett., 37:11 (1976), 693–697 | DOI | MR

[8] R. Hirota, J. Satsuma, J. Phys. Soc. Japan, 41:6 (1976), 2141–2142 | DOI

[9] F. Calogero, A. Degasperis, Comm. Math. Phys., 63:2 (1978), 155–176 | DOI | MR | Zbl

[10] M. R. Gupta, Phys. Lett. A, 72:6 (1979), 420–422 | DOI | MR

[11] M. Wadati, K. Konno, Y. H. Ichikawa, J. Phys. Soc. Japan, 46:6 (1979), 1965–1966 | DOI | MR | Zbl

[12] S. P. Burtsev, V. E. Zakharov, A. V. Mikhailov, TMF, 70:3 (1987), 323–341 | DOI | MR | Zbl

[13] V. E. Adler, A. B. Shabat, R. I. Yamilov, TMF, 125:3 (2000), 355–424 | DOI | MR | Zbl

[14] T.-K. Ning, D.-J. Zhang, D.-Y. Chen, S.-F. Deng, Chaos Solitons Fractals, 25:3 (2005), 611–620 | DOI | MR | Zbl

[15] S.-F. Deng, D.-J. Zhang, D.-Y. Chen, J. Phys. Soc. Japan, 74:9 (2005), 2383–2385 | DOI | MR | Zbl

[16] S.-F. Deng, Z.-Y. Qin, Phys. Lett. A, 357:6 (2006), 467–474 | DOI | MR | Zbl

[17] D.-J. Zhang, J. Phys. Soc. Japan, 71:11 (2002), 2649–2656 | DOI | MR | Zbl

[18] D.-J. Zhang, Chaos Solitons Fractals, 18:1 (2003), 31–43 | DOI | MR | Zbl

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

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

[21] D.-J. Zhang, J.-B. Bi, H.-H. Hao, J. Phys. A, 39:47 (2006), 14627–14648 | DOI | MR | Zbl

[22] J. W. Miles, J. Fluid Mech., 79:1 (1977), 171–179 | DOI | Zbl

[23] K. Ohkuma, M. Wadati, J. Phys. Soc. Japan, 52:3 (1983), 749–760 | DOI | MR

[24] J. Hietarinta, “Scattering of solitons and dromions”, Scattering: Scattering and Inverse Scattering in Pure and Applied Science, V. 2, eds. R. Pike, P. Sabatier, Academic Press, London, 2002, 1773–1791 | MR | Zbl

[25] R. Hirota, The Direct Method in Soliton Theory, Cambridge Tracts in Math., 155, Cambridge Univ. Press, Cambridge, 2004 | MR | Zbl

[26] N. C. Freeman, J. J. C. Nimmo, Phys. Lett. A, 95:1 (1983), 1–3 | DOI | MR

[27] R. Hirota, J. Satsuma, Phys. Lett. A, 85:8–9 (1981), 407–408 | DOI | MR