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Czasopismo
2014 | 12 | 2 | 81-89
Tytuł artykułu

Nonlinear self-adjointness and invariant solutions of a 2D Rossby wave equation

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The paper investigates the nonlinear self-adjointness of the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane. It is a particular form of Rossby equation which does not possess variational structure and it is studied using a recently method developed by Ibragimov. The conservation laws associated with the infinite-dimensional symmetry Lie algebra models are constructed and analyzed. Based on this Lie algebra, some classes of similarity invariant solutions with nonconstant linear and nonlinear shears are obtained. It is also shown how one of the conservation laws generates a particular wave solution of this equation.
Wydawca
Czasopismo
Rocznik
Tom
12
Numer
2
Strony
81-89
Opis fizyczny
Daty
wydano
2014-02-01
online
2014-02-15
Twórcy
  • University of Craiova, 13 A.I.Cuza, 200585, Craiova, Romania
Bibliografia
  • [1] W. F. Ames, Nonlinear Partial Differential Equations in Engineering II, (Academic Press, New York, 1972)
  • [2] G. W. Bluman, S. Kumei, Symmetries and Differential Equations, (Springer-Verlag, New York, 1989) http://dx.doi.org/10.1007/978-1-4757-4307-4[Crossref]
  • [3] P. E. Hydon, Symmetry Methods for Differential Equations, (Cambridge Texts in Applied Mathematics, Cambridge University Press, 2000) http://dx.doi.org/10.1017/CBO9780511623967[Crossref]
  • [4] N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics, (Dordrecht: Reidel, 1985) http://dx.doi.org/10.1007/978-94-009-5243-0[Crossref]
  • [5] F. Kangalgil, F. Ayaz, Phys. Lett. A 372, 1831 (2008) http://dx.doi.org/10.1016/j.physleta.2007.10.045[Crossref]
  • [6] R. Cimpoiasu, R. Constantinescu, J. Nonlin. Math. Phys. 13, 285 (2006) http://dx.doi.org/10.2991/jnmp.2006.13.2.10[Crossref]
  • [7] C. Korögluand, T. Özis, Comput. Math. Appl. 58, 2142 (2009) http://dx.doi.org/10.1016/j.camwa.2009.03.028[Crossref]
  • [8] P. J. Olver, Application of Lie Groups to Differential Equations, (Springer, New-York, 1986) http://dx.doi.org/10.1007/978-1-4684-0274-2[Crossref]
  • [9] A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, Dokl. Akad. nauk SSSR 295, 288 (1987)
  • [10] A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, Commun. Math. Phys. 115, 1 (1988) http://dx.doi.org/10.1007/BF01238850[Crossref]
  • [11] Y. Kodama, A. V. Mikhailov, Obstacles to Asymptotic Integrability in Algebraic aspects of Integrability, (Birkhauser, Boston Basel, Berlin, 1996)
  • [12] R. J. LeVeque, Numerical Methods for Conservation Laws, (Lectures in Mathematics: ETH Zurich, Birkhauser Verlag, 1992) http://dx.doi.org/10.1007/978-3-0348-8629-1[Crossref]
  • [13] B. Cockburn, S. Hou, C. Wang Shu, Math. Comput. 54, 545 (1990)
  • [14] S. C. Anco, G. Bluman, J. Math. Phys. 37, 2361 (1996) http://dx.doi.org/10.1063/1.531515[Crossref]
  • [15] A. H. Kara, F. M. Mahomed, Int. J. Theor. Phys. 39, 23 (2000) http://dx.doi.org/10.1023/A:1003686831523[Crossref]
  • [16] N. H. Ibragimov, J. Phys. A: Math. Theor. 44, 432002 (2011) http://dx.doi.org/10.1088/1751-8113/44/43/432002[Crossref]
  • [17] M. S. Bruzon, M. L. Gandarias, N. H. Ibragimov, J. Math. Anal. Appl. 357, 307 (2009) http://dx.doi.org/10.1016/j.jmaa.2009.04.028[Crossref]
  • [18] N. H. Ibragimov, Archives of ALGA 7/8, 1 (2011)
  • [19] M. Torrisi, R. Tracina, Nonlinear Anal-Theor 14, 1496 (2013) http://dx.doi.org/10.1016/j.nonrwa.2012.10.013[Crossref]
  • [20] Y. Lee, L. M. Smith, Physica D 179, 53 (2003) http://dx.doi.org/10.1016/S0167-2789(03)00010-1[Crossref]
  • [21] D. A. Siegel, Nature 409, 576 (2001) http://dx.doi.org/10.1038/35054659[Crossref]
  • [22] D. Luo, F. Huang, Y. Diao, J. Geophys. Res. Atmos. 106, 31795 (2001) http://dx.doi.org/10.1029/2000JD000086[Crossref]
  • [23] J. Pedlosky, Geophysical Fluid Dynamics, (Springer, New-York, 1979) http://dx.doi.org/10.1007/978-1-4684-0071-7[Crossref]
  • [24] W. I. Fushchych, W. M. Shtelen, S. L. Slavutsky, J. Phys. A: Math. Gen. 24, 971 (1991) http://dx.doi.org/10.1088/0305-4470/24/5/012[Crossref]
  • [25] G. E. Swaters, Geophys. Astrophys. Fluid Dyn. 36, 85 (1986) http://dx.doi.org/10.1080/03091928608208798[Crossref]
  • [26] F. Huang, S. Y. Lou, Phys. Lett. A 320, 428 (2004) http://dx.doi.org/10.1016/j.physleta.2003.11.056[Crossref]
  • [27] R. Constantinescu, J. Math. Phys. 38, 2786 (1997) http://dx.doi.org/10.1063/1.532019[Crossref]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_s11534-014-0430-6
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