Geodesic
Conservation laws and symmetry analysis of (1+1)-dimensional Sawada-Kotera equation
Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2017), pp. 10-19 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper addresses an extended (1+1)-dimensional Sawada-Kotera (SK) equation. The Lie symmetry analysis leads to many plethora of solutions to the equation. The non-linear self-adjointness condition for the SK equation established and subsequently used to construct simplified independent conserved vectors. In particular, we also get conservation laws of the equation with the corresponding Lie symmetry.
Keywords: Fluid mechanics, Lie symmetry, Partial differential equation, Shear stress, Optimal system, Partial differential equation, KdV equation, Lie symmetry, Conservation Laws. 
@article{VKAM_2017_3_a1,
     author = {R.S. Hejazi and E. Lashkarian},
     title = {Conservation laws and symmetry analysis of (1+1)-dimensional {Sawada-Kotera} equation},
     journal = {Vestnik KRAUNC. Fiziko-matemati\v{c}eskie nauki},
     pages = {10--19},
     year = {2017},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VKAM_2017_3_a1/}
}
TY  - JOUR
AU  - R.S. Hejazi
AU  - E. Lashkarian
TI  - Conservation laws and symmetry analysis of (1+1)-dimensional Sawada-Kotera equation
JO  - Vestnik KRAUNC. Fiziko-matematičeskie nauki
PY  - 2017
SP  - 10
EP  - 19
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VKAM_2017_3_a1/
LA  - en
ID  - VKAM_2017_3_a1
ER  - 
%0 Journal Article
%A R.S. Hejazi
%A E. Lashkarian
%T Conservation laws and symmetry analysis of (1+1)-dimensional Sawada-Kotera equation
%J Vestnik KRAUNC. Fiziko-matematičeskie nauki
%D 2017
%P 10-19
%N 3
%U http://geodesic.mathdoc.fr/item/VKAM_2017_3_a1/
%G en
%F VKAM_2017_3_a1
R.S. Hejazi; E. Lashkarian. Conservation laws and symmetry analysis of (1+1)-dimensional Sawada-Kotera equation. Vestnik KRAUNC. Fiziko-matematičeskie nauki, no. 3 (2017), pp. 10-19. http://geodesic.mathdoc.fr/item/VKAM_2017_3_a1/

[1] Alexandrova A. A., Ibragimov N. H., Imamutdinova K. V., Lukashchuk V. O., “Local and nonlocal conserved vectors for the nonlinear filtration equation”, Ufa Math J.. 9:4 (2012), 179–85 | MR

[2] Kerishnan E. V., “On Sawada-Kotera equations”, II Nuovo Cimento B, 92:1, 23-26 | DOI | MR

[3] Bluman G. W., Cheviakov A. F., Anco C., “Construction of Conservation Laws: How the Direct Method Generalizes Noether's Theorem”, Proceeding of 4th Workshop “Group Analysis of Differential Equations Integribility”, 2009, 1–23 | MR

[4] Bluman G. W., Cheviakov A. F., Anco C., Application of Symmetry Methods to Partial Differential Equations, Springer, New York, 2000 | MR

[5] Bluman G. W., Cole J. D., “The general similarity solution of the heat equation”, J. Math. Mech., 18 (1969), 1025–1042 | MR | Zbl

[6] Fushchych W. I., Popovych R. O., “Symmetry reduction and exact solutions of the Navier–Stokes equations”, J. Nonlinear Math. Phys., 1:75–113 (1994), 156–188 | MR

[7] Hejazi S. R., “Lie group analaysis, Hamiltonian equations and conservation laws of Born–Infeld equation”, Asian-European Journal of Mathematics, 7:3 (2014), 1450040 | DOI | MR | Zbl

[8] Hydon P. E., Stmmetry Method for Differential Equations, Cambridge University Press, UK, Cambridge, 2000 | MR

[9] Ibragimov N. H., Transformation group applied to mathematical physics, Riedel, Dordrecht, 1985 | MR

[10] Ibragimov N. H., Aksenov A V., Baikov V. A., Chugunov V. A. , Gazizov R. K. and Meshkov A. G., CRC handbook of Lie group analysis of differential equations. Applications in engineering and physical sciences, v. 2, CRC Press, Boca Raton, 1995 | MR | Zbl

[11] Ibragimov N. H., “Nonlinear self-adjointness in constructing conservation laws”, Arch ALGA, 7/8 (2010–2011), 1–99

[12] Ibragimov N. H., Anderson R. L., “Lie theory of differential equations”, Lie group analysis of differential equations. Symmetries, exact solutions and conservation laws., v. 1, CRC Press, Boca Raton, 1994, 7–14 | MR

[13] Ibragimov N. H., N Arch ALGA 2010–2011, 7/8, 1–99 | Zbl

[14] Li J. B., Wu J. H. and Zhu H. P., “Travelling Waves for an Integrable Higher Order KdV Type Wave Equation”, Int. J. Bifur Chaos Appl. Sci. Eng., 2006, 2235–2260 | MR | Zbl

[15] Nadjafikhah M., Hejazi S. R., “Symmetry analysis of cylindrical Laplace equation”, Balkan journal of geometry and applications, 2009 | MR

[16] Olver P. J., Equivalence, Invariant and Symmetry, Cambridge, Cambridge University Press, 1995 | MR

[17] Ovsiannikov L. V., Group Analysis of Differential Equations, Academic Press, New York, 1982 | MR | Zbl

[18] Zwillinger D., Handbook of Differential Equations, Academic Press, Boston, 1997, 132 pp. | MR