Conservation laws and similarity reduction of the Zoomeron equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2016), pp. 7-13 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this study, we consider a 4-th order (1+1)-dimensional PDE called Zoomeron equation. Some conservation laws are derived based on direct method. We also derived some similarity solutions using the symmetries.
Keywords: Lie point symmetries, conservation laws, similarity solution.
Mots-clés : Zoomeron equation, multiplier
@article{VKAM_2016_3_a0,
     author = {S. Hejazi and A. Naderifard and S. Rashidi},
     title = {Conservation laws and similarity reduction of the {Zoomeron} equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {7--13},
     year = {2016},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2016_3_a0/}
}
TY  - JOUR
AU  - S. Hejazi
AU  - A. Naderifard
AU  - S. Rashidi
TI  - Conservation laws and similarity reduction of the Zoomeron equation
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2016
SP  - 7
EP  - 13
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VKAM_2016_3_a0/
LA  - en
ID  - VKAM_2016_3_a0
ER  - 
%0 Journal Article
%A S. Hejazi
%A A. Naderifard
%A S. Rashidi
%T Conservation laws and similarity reduction of the Zoomeron equation
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2016
%P 7-13
%N 3
%U http://geodesic.mathdoc.fr/item/VKAM_2016_3_a0/
%G en
%F VKAM_2016_3_a0
S. Hejazi; A. Naderifard; S. Rashidi. Conservation laws and similarity reduction of the Zoomeron equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2016), pp. 7-13. http://geodesic.mathdoc.fr/item/VKAM_2016_3_a0/

[1] Calogero F., Degasperis A., “Non-linear evolution equations solvable by the inverse spectral transform I”, Nuovo Cimento B, 32 (1976), 201-242 | DOI | MR

[2] Bluman G., Cheviakov A., Anco C., “Applications of Symmetry Methods to partial Differential Equations”, Appl. Math. Sci, 168 (2010), 43-70 | MR

[3] Craddock M., Lennox K., “Lie group symmetries as integral transforms of fundamental solutions”, J. Differential Equations, 232:2 (2007), 652-674 | DOI | MR | Zbl

[4] Abazari R., “The solitary wave solutions of Zoomeron equation”, Appl. Math. Sci., 5 (2011), 2943-2949 | MR | Zbl

[5] Alquran M., Al-Khaled K., “Mathematical methods for a reliable treatment of the (2+1)-dimensional Zoomeron equation”, Math. Sci., 6 (2012), 11-15 | DOI | MR

[6] Craddock M., Platen E., “Symmety group methods for fundamental solutions”, J. Differential Equations, 207:2 (2007), 285-302 | DOI | MR

[7] Liu H. Z. , Li J. B., “Symmetry reductions, dynamical behavior and exact explicit solutions to the Gordon types of equations”, J. Comput. Appl. Math., 257 (2014), 144-156 | DOI | MR | Zbl

[8] Olver P., Applications of Lie Groups to Differential Equations, Grad. Texts in Math., 107, Springer, New York, 1993 | DOI | MR | Zbl

[9] Ibragimov N. H., “Nonlinear self-adjointness in constructing conservation laws”, Archives of ALGA, 7-8 (2010-2011), 1-99