Geodesic
Traveling-Wave Solutions of the Calogero–Degasperis–Fokas Equation in $2+1$ Dimensions
Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 44-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Soliton solutions are among the more interesting solutions of the $(2+1)$-dimensional integrable Calogero–Degasperis–Fokas (CDF) equation. We previously derived a complete group classiffication for the CDF equation in $2+1$ dimensions. Using classical Lie symmetries, we now consider traveling-wave reductions with a variable velocity depending on an arbitrary function. The corresponding solutions of the $(2+1)$-dimensional equation involve up to three arbitrary smooth functions. The solutions consequently exhibit a rich variety of qualitative behaviors. Choosing the arbitrary functions appropriately, we exhibit solitary waves and bound states.
Keywords: Lie symmetries, partial differential equations, solitary waves. 
@article{TMF_2005_144_1_a4,
     author = {M. L. Gandarias and S. Saez},
     title = {Traveling-Wave {Solutions} of the {Calogero{\textendash}Degasperis{\textendash}Fokas} {Equation} in $2+1$ {Dimensions}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {44--55},
     year = {2005},
     volume = {144},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a4/}
}
TY  - JOUR
AU  - M. L. Gandarias
AU  - S. Saez
TI  - Traveling-Wave Solutions of the Calogero–Degasperis–Fokas Equation in $2+1$ Dimensions
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2005
SP  - 44
EP  - 55
VL  - 144
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a4/
LA  - ru
ID  - TMF_2005_144_1_a4
ER  - 
%0 Journal Article
%A M. L. Gandarias
%A S. Saez
%T Traveling-Wave Solutions of the Calogero–Degasperis–Fokas Equation in $2+1$ Dimensions
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2005
%P 44-55
%V 144
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a4/
%G ru
%F TMF_2005_144_1_a4
M. L. Gandarias; S. Saez. Traveling-Wave Solutions of the Calogero–Degasperis–Fokas Equation in $2+1$ Dimensions. Teoretičeskaâ i matematičeskaâ fizika, Tome 144 (2005) no. 1, pp. 44-55. http://geodesic.mathdoc.fr/item/TMF_2005_144_1_a4/

[1] K. Toda, S. Yu, Rep. Math. Phys., 48 (2001), 255 | DOI | MR | Zbl

[2] F. Calogero, A. Degasperis, J. Math. Phys., 22 (1981), 23 | DOI | MR | Zbl

[3] A. S. Fokas, J. Math. Phys., 21 (1980), 1318 | DOI | MR | Zbl

[4] A. Nakamura, R. Hirota, J. Phys. Soc. Japan, 48 (1980), 1755 | DOI | MR | Zbl

[5] K. M. Tamizhmani, M. Lakshmanan, Phys. Lett. A, 90 (1982), 159 | DOI | MR

[6] P. Rosenau, Phys. Lett. A, 211 (1996), 265 | DOI | MR | Zbl

[7] W. K. Schief, C. Rogers, Proc. Roy. Soc. Lond. A, 455 (1999), 3163 | DOI | MR | Zbl

[8] M. V. Pavlov, Phys. Lett. A, 243 (1998), 245 | DOI | MR

[9] H. H. Chen, Phys. Rev. Lett., 33 (1974), 925 | DOI | MR | Zbl

[10] K. Toda, S. Yu, J. Math. Phys., 41 (2000), 4747 | DOI | MR | Zbl

[11] D. David, N. Kamran, D. Levi, P. Winternitz, J. Math. Phys., 27 (1986), 1225 | DOI | MR | Zbl

[12] D. Levi, P. Winternitz, Phys. Lett. A, 129 (1988), 165 | DOI | MR

[13] M. Senthil Velan, M. Lakshmanan, J. Nonlin. Math. Phys., 5 (1998), 190 | DOI | MR | Zbl

[14] J. Ramirez, M. S. Bruzon, C. Muriel, M. L. Gandarias, J. Phys. A, 36 (2002), 1467 | DOI | MR

[15] E. L. Ains, Obyknovennye differentsialnye uravneniya, DNTVU, Kharkov, 1939 | MR