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Articles

On the discretization of Darboux Integrable Systems

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Pages 616-632 | Received 02 Jul 2019, Accepted 06 Jan 2020, Published online: 04 Sep 2020

References

  • A.V. Zhiber, R.D. Murtazina, I.T. Habibullin, and A.B. Shabat, Characteristic Lie rings and integrable models in mathematical physics, Ufa Math. J., 4 (3) (2012) 17–85.
  • I.T. Habibullin, N. Zheltukhina, and A. Sakieva, Discretization of hyperbolic type Darboux integrable equations preserving integrability, J. Math. Phys., 52 (2011) 093507–093519. doi: 10.1063/1.3628587
  • I.T. Habibullin and N. Zheltukhina, Discretization of Liouville type nonautonomous equations, J. Nonlinear Math. Phys., 23 (2016) 620–642. doi: 10.1080/14029251.2016.1248159
  • K. Zheltukhin and N. Zheltukhina, On the discretization of Laine equations, J. Nonlinear Math. Phys., 25 (2018) 166–177. doi: 10.1080/14029251.2018.1440748
  • I.T. Habibullin, A. Pekcan, Characteristic Lie algebra and the classification of semi-discrete models, Theoret. and Math. Phys., 151 (2007) 781–790. doi: 10.1007/s11232-007-0064-6
  • O.S. Kostrigina and A.V. Zhiber, Darboux-integrable two-component nonlinear hyperbolic systems of equations, J. Math. Phys., 52 (2011) 033503–033535. doi: 10.1063/1.3559134
  • A.B. Shabat and R.I. Yamilov, Exponential Systems of Type I and the Cartan Matrices (Russian), Preprint BBAS USSR Ufa (1981).
  • N.H. Ibragimov, A.V. Aksenov, V.A. Baikov, V.A. Chugunov, R.K. Gazizov and A.G. Meshkov, CRC Handbook of Lie Group Analysis of Differential Equations, Vol. 2., Applications in Engineeringand Physical Science, edited by Ibragimov, Boca Raton, FL: CRC Press (1995).
  • E.I. Ganzha and S.P. Tsarev, Integration of Classical Series An, Bn, Cn, of Exponential Systems, Krasnoyarsk: Krasnoyarsk State Pedagogical University Press (2001).
  • A.N. Leznov and M.V. Savel’ev, Group Methods of Integration of Nonlinear Dynamical Systems, Progress in Physics 15, Birkhäuser Verlag, Basel (1992).
  • I.T. Habibullin, K. Zheltukhin, and M. Yangubaeva, Cartan matrices and integrable lattice Toda field equations, J. Phys. A, 44 (2011) 465202–465222. doi: 10.1088/1751-8113/44/46/465202

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