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Differential-Invariant Solutions

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We construct differential-invariant solutions to automorphic systems and propose a method for classifying differential-invariant submodels.

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References

  1. L. V. Ovsyannikov, Group Analysis of Differential Equations, Academic Press, New York (1982).

    MATH  Google Scholar 

  2. A. A. Talyshev, “On automorphic systems of finite-dimensional Lie groups,” Ufa Math. J. 4, No. 4, 127–134 (2012).

    MathSciNet  MATH  Google Scholar 

  3. A. A. Talyshev, “On integration of automorphic systems of finite-dimensional Lie groups,” Ufa Math. J. 6, No. 1, 104–110 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  4. S. V. Khabirov, “Classification of differential invariant submodels,” Sib. Math. J. 45, No. 3, 562–579 (2004).

    Article  MATH  Google Scholar 

  5. S. V. Golovin, “Group stratification and exact solutions of the equation of transonic gas motion,” J. Appl. Mech. Tech. Phys. 44, No. 3, 344–354 (2003).

    Article  MathSciNet  Google Scholar 

  6. L. V. Ovsyannikov, “‘Simple’ solutions of the equations of dynamics for a polytropic gas,” J. Appl. Mech. Tech. Phys. 40, No. 2. 191–197 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  7. L. V. Ovsyannikov, “The “PODMODELI” program. Gas dynamics,” J. Appl. Math. Mech. 58, No. 4, 601–627 (1994).

    Article  MathSciNet  MATH  Google Scholar 

  8. L. V. Ovsyannikov, “Hierarchy of invariant submodels of differential equations,” Dokl. Math. 58, No. 1, 127–129 (1998).

    MATH  Google Scholar 

  9. K. K. Izmaylova and A. P. Chupakhin, “Group theoretical solutions of the Schrödinger equation generated by three-dimensional symmetry algebras” [in Russian], Nelin. Dinam. 3, No. 3, 349–362 (2007).

    Article  Google Scholar 

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Correspondence to A. A. Talyshev.

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Translated from Sibirskii Zhurnal Chistoi i Prikladnoi Matematiki 16, No. 3, 2016, pp. 75-84.

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Talyshev, A.A. Differential-Invariant Solutions. J Math Sci 230, 167–174 (2018). https://doi.org/10.1007/s10958-018-3736-x

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  • DOI: https://doi.org/10.1007/s10958-018-3736-x

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