Geodesic
Solitons of the resonant nonlinear Schrödinger equation with
Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 133-146

Voir la notice de l'article provenant de la source Math-Net.Ru

We use the Hirota bilinear approach to consider physically relevant soliton solutions of the resonant nonlinear Schrödinger equation with nontrivial boundary conditions, recently proposed for describing uniaxial waves in a cold collisionless plasma. By the Madelung representation, the model transforms into the reaction–diffusion analogue of the nonlinear Schrödinger equation, for which we study the bilinear representation, the soliton solutions, and their mutual interactions.
Keywords: resonant nonlinear Schrödinger equation, quantum potential, cold plasma, magnetoacoustic wave, Hirota method.
Mots-clés : soliton 
J.-H. Lee; O. K. Pashaev. Solitons of the resonant nonlinear Schrödinger equation with. Teoretičeskaâ i matematičeskaâ fizika, Tome 152 (2007) no. 1, pp. 133-146. http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a9/
@article{TMF_2007_152_1_a9,
     author = {J.-H. Lee and O. K. Pashaev},
     title = {Solitons of the~resonant nonlinear {Schr\"odinger} equation with},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {133--146},
     year = {2007},
     volume = {152},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a9/}
}
TY  - JOUR
AU  - J.-H. Lee
AU  - O. K. Pashaev
TI  - Solitons of the resonant nonlinear Schrödinger equation with
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2007
SP  - 133
EP  - 146
VL  - 152
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a9/
LA  - ru
ID  - TMF_2007_152_1_a9
ER  - 
%0 Journal Article
%A J.-H. Lee
%A O. K. Pashaev
%T Solitons of the resonant nonlinear Schrödinger equation with
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2007
%P 133-146
%V 152
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2007_152_1_a9/
%G ru
%F TMF_2007_152_1_a9

[1] O. K. Pashaev, J.-H. Lee, Mod. Phys. Lett. A, 17 (2002), 1601–1619 | DOI | Zbl

[2] L. de Broglie, C. R. Acad. Sci. Paris, 183 (1926), 447–448 | Zbl

[3] D. Bohm, Phys. Rev., 85 (1952), 166–179 ; 180–193 | DOI | MR | Zbl | DOI | MR

[4] E. Nelson, Phys. Rev., 150 (1966), 1079–1085 | DOI

[5] G. Salesi, Mod. Phys. Lett. A, 11 (1996), 1815–1823 | DOI | MR | Zbl

[6] F. Guerra, M. Pusterla, Lett. Nuovo Cimento (2), 34 (1982), 351–356 | DOI | MR

[7] L. Smolin, Phys. Lett. A, 113:8 (1986), 408–412 | DOI | MR

[8] O. Bertolami, Phys. Lett. A, 154 (1991), 225–229 | DOI

[9] L. K. Antanovskii, C. Rogers, W. K. Schief, J. Phys. A, 30 (1997), L555–L557 | DOI | MR | Zbl

[10] C. Rogers, W. K. Schief, Nuovo Cimento B, 114 (1999), 1409–1412

[11] J.-H. Lee, O. K. Pashaev, C. Rogers, W. K. Schief, J. Plasma Phys., 73:02 (2007), 257–272 | DOI

[12] V. I. Karpman, Nelineinye volny v dispergiruyuschikh sredakh, Nauka, M., 1973 | MR | MR

[13] A. I. Akhiezer, I. A. Akhiezer, R. V. Polovin, A. G. Sitenko, K. N. Stepanov, Elektrodinamika plazmy, Nauka, M., 1974 | Zbl

[14] J. H. Adlam, J. E. Allen, Philos. Mag., 3 (1958), 448–455 | DOI | Zbl

[15] A. V. Gurevich, A. P. Mescherkin, ZhETF, 87 (1984), 1277–1292

[16] G. A. El, V. V. Khodorovskii, A. V. Tyurina, Phys. Lett. A, 333 (2004), 334–340 | DOI | Zbl

[17] A. V. Gurevich, A. L. Krylov, ZhETF, 92 (1987), 1684–1699

[18] A. V. Gurevich, A. L. Krylov, Dokl. AN SSSR, 298 (1988), 608–611 | Zbl

[19] G. A. El, R. H. J. Grimshaw, M. V. Pavlov, Stud. Appl. Math., 106 (2001), 157–186 | DOI | MR | Zbl

[20] R. Hirota, “Direct method of finding exact solutions of nonlinear evolution equations”, Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications (Nashville, 1974), Lecture Notes in Math., 515, ed. R. M. Miura, Springer, Berlin, 1976, 40–68 | DOI | MR | Zbl