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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Nonlinear Self-adjointness for a Generalized Fisher Equation in Cylindrical Coordinates

Journal of Applied Nonlinear Dynamics 4(1) (2015) 91--100 | DOI:10.5890/JAND.2015.03.008

M.L. Gandarias; M.S. Bruzón; M. Rosa

Departamento de Matemáticas, Universidad de Cádiz, Polígono del Río San Pedro, 11510, Puerto Real, Cádiz, Spain

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Abstract

In this work we study a generalization of the well known Fisher equation in cylindrical coordinates. We determine the subclasses of these equations which are nonlinear self-adjoint. By using a general theorem on conservation laws proved by Nail Ibragimov and the symmetry generators we find conservation laws for these partial differential equations without classical Lagrangians.

References

  1. [1]  Murray, J.D. (2002), Mathematical Biology, 3rd Edition, Springer-Verlag, New York, Berlin, Heidelberg.
  2. [2]  Britton, N.F. (1989), Aggregation and the competitive exclusion principle, Journal of Theoretical Biology, 136, 57-66.
  3. [3]  Vinogradov, A.M. (1984), Local symmetries and conservation law. Acta Applicandae Mathematicae, 2, 21-78.
  4. [4]  Anco, S.C. and Bluman, G. (2002), Direct construction method for conservation laws for partial differential equations Part II: General treatment, Journal of Applied Mathematics, 41, 567-585.
  5. [5]  Ibragimov N.H. (2007), A new conservation theorem. Journal of Mathematical Analysis and Applications, 333, 311-328.
  6. [6]  Ibragimov, N.H. (2006), The answer to the question put to me by LV Ovsiannikov 33 years ago, Arch. ALGA, 3, 53-80.
  7. [7]  Ibragimov, N.H. (2007), Quasi-self-adjoint differential equations, Arch. ALGA, 4, 55-60.
  8. [8]  Gandarias, M.L. (2011) Weak self-adjoint differential equations, Journal of Physics A: Mathematical and Theoretical, 44, 262001.
  9. [9]  Ibragimov, N.H. (2011), Nonlinear self-adjointness and conservation laws, Journal of Physics A: Mathematical and Theoretical, 44, 432002.
  10. [10]  Gandarias, M.L. (2013), Nonlinear self-adjointness and conservation laws for a generalized Fisher equation, Communications in Nonlinear Science and Numerical Simulation, 18, 1600-1606.
  11. [11]  Moitsheki, R.J. and Makinde, O.D. (2011), Classical Lie point symmetry analysis of nonlinear diffusion equations describing thermal energy storage, Communications in Nonlinear Science and Numerical Simulation, 16, 2689.
  12. [12]  Bokhari, A.H., Mustafá, M.T., and Zaman, F.D (2008), An exact solution of a quasilinear Fisher equation in cylindrical coordinates, Nonlinear Analysis, 69, 4803-4805.
  13. [13]  Bokhari, A.H., Al-Rubaee, R.A., and Zaman, F.D. (2011), On a generalized Fisher equation Communications in Nonlinear Science and Numerical Simulation , 16, 2689.
  14. [14]  Olver, P.J. (1986), Aplications of Lie Groups to Differential Equations, Springer-Verlag.

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