Majors About the New Symmetry of a Nonlinear Acoustics Model
New Symmetry
DOI:
https://doi.org/10.55672/hij2022pp1-6Keywords:
Zabolotskaya- Khokhlov equation (ZK), Symmetry algebra, Lie point symmetry group, Optimal system of subalgebras, Reduction of equationAbstract
The Lie symmetry group of the Zabolotskaya-Khokhlov equation has been seriously studied, earlier than this. Eventually, it has been endowed with a general model by N.J.C. Ndogmo, in 2008. This research is devoted to introducing the algebra, the group, and the reductions of a new symmetry which is an exception of that model.
Downloads
References
J.C. Ndogmo, Symmetry properties of a nonlinear acoustics model, Nonlinear Dyn. 55
(2009),151-167.
E.A. Zabolotskaya , R.V. Khokhlov, Quasi plane waves in the nonlinear acoustics of
confined beams, Sov. Phys. Acoust. 15 (1969), 35{40.
A.P. Sarvazyan, O.V. Rudenko, S.D. Swanson, J.B. Fowlkes, S.Y. Emelianov, Shear
wave elasticity imaging, A new ultrasonic technology of medical diagnostics, Ultrasound
Med. Biol. 24 (1999), 1419{1435.
N.S. Bakhvalov, Y.M. Zhileikin, E. A. Zabolotskaya, Nonlinear theory of sound beams,
Am. Inst. Phys, NewYork, 1987.
A.R. Chowdhury, M. Nasker, Towards the conservation laws and Lie symmetries for the
Khokhlov-Zabolotskaya equation in three dimensions, J. Phys. A: Math. Gen. 19 (1986),
{1782.
F.Schwarz, Symmetries of the Khokhlov-Zabolotskaya equation, J. Phys. A: Math. Gen.
(1987), 1613{1614.
W.Herman, W.H. Steeb, N.Euler, Towards the conservation laws and Lie symmetries
for the Khokhlov-Zabolotskaya equation in three dimensions, J. Phys. A: Math. Gen. 25
(1992), 2417{2418.
J.F. Zhang, Y.J. Zhu, J. Lin, Similarity reductions of the Khokhlov-Zabolotskaya equation, Commun. Theor. Phys. 24 (1995), 69-74.
P.A. Clarkson, M.D Kruskal, New similarity reductions of the boussinesq equation, J.
Math. Phys. 30 (1989), 2201{2213.
P.J. Olver, Applications of Lie groups to differential equations, Springer, NewYork,
P.J. Olver, Equivalence, invariants, and symmetry, Cambridge University Press, Cambridge, 1995.
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 HyperScience International Journal
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
