Application of the quasi-spectral fourier method to soliton equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2176-2183 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A numerical approach combining the quasi-spectral Fourier method and the Runge–Kutta technique is proposed for the numerical study of the long wavelength regularized equation and the Camassa–Holm and Holm–Hone equations. Test results are presented for soliton and peakon solutions.
@article{ZVMMF_2010_50_12_a7,
     author = {S. P. Popov},
     title = {Application of the quasi-spectral fourier method to soliton equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2176--2183},
     year = {2010},
     volume = {50},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a7/}
}
TY  - JOUR
AU  - S. P. Popov
TI  - Application of the quasi-spectral fourier method to soliton equations
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 2176
EP  - 2183
VL  - 50
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a7/
LA  - ru
ID  - ZVMMF_2010_50_12_a7
ER  - 
%0 Journal Article
%A S. P. Popov
%T Application of the quasi-spectral fourier method to soliton equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 2176-2183
%V 50
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a7/
%G ru
%F ZVMMF_2010_50_12_a7
S. P. Popov. Application of the quasi-spectral fourier method to soliton equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 12, pp. 2176-2183. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_12_a7/

[1] Benjamin T. B., Bona J. G., Mahony J. J., “Model equations for long waves in nonlinear dispersive systems”, Philos. Trans. Roy. Soc., 272A (1972), 47–78 | MR | Zbl

[2] Camassa R., Holm D., “An intergrable shallow water equation with peaked soliton”, Phys. Rev. Letts., 71 (1993), 1661–1664 | DOI | MR | Zbl

[3] Dai H.-H., “Model equations for nonlinear dispersive waves in a compressible Money–Rivlin rod”, Acta Mech., 127:1–4 (1998), 193–207 | DOI | MR | Zbl

[4] Kholm D. D., Khon A. N. V., “Integriruemost uravneniya pyatogo poryadka s integriruemoi dinamikoi dvukh tel”, Teor. i matem. fiz., 137:1 (2003), 121–136 | MR

[5] Duran A., Lopez-Marcos M. A., “Conservative numerical methods for solitary wave interaction”, J. Phys. A: Math. Gen., 2003, no. 36, 7761–7770 | DOI | MR | Zbl

[6] Zhou Y., “Wave breaking for shallow water equation”, Nonlinear Analys., 57 (2004), 137–152 | DOI | MR | Zbl

[7] Bogoyavlenskii O. I., Oprokidyvayuschiesya solitony, Nauka, M., 1991 | MR | Zbl

[8] Hui-Hui Dai, Yishen Li, “The interaction of the $\omega$-soliton and $\omega$-cuspon of the Camassa–Holm equation”, J. Phys. A: Math. Gen., 2005, no. 42, L685–L694 | MR | Zbl