Alim Sukhtayev, Assistant Professor

Department of Mathematics
Miami University

Office: 226 BAC
Phone: (513) 529-2189


Research Interests 

Curriculum Vitae


  1. Instability of pulses in gradient reaction--diffusion systems: A symplectic approach, to appear in Philosophical Transactions of the Royal Society A
    (with M. Beck, G. Cox, C. Jones, Y. Latushkin, K. McQuighan) arXiv:1705.03861

  2. Diffusive stability of spatially periodic patterns with a conservation law, submitted arXiv:1610.05395

  3. Diffusive stability of spatially periodic solutions of the Brusselator model, submitted (with K. Zumbrun, S. Jung, R. Venkatraman) arXiv:1608.08476

  4. The Maslov and Morse indices for Schr\"odinger operators on $\mathbb{R}$, to appear in Indiana University Mathematics Journal (with P. Howard, Y. Latushkin) arXiv:1608.05692

  5. The Maslov and Morse indices for Lagrangian pairs on $\mathbb{R}^{2n}$, J. Math. Anal. Appl. 451 (2017), no. 2, 794-821. (with P. Howard, Y. Latushkin) arXiv:1608.00632

  6. Hadamard-type formulas via the Maslov form, J. Evol. Equ. 17 (2017), no. 1, 443-472. (with Y. Latushkin) arXiv:1601.07509

  7. The Maslov and Morse indices for Schr\"odinger Operators on $[0,1]$, Journal of Differential Equations 260 (2016), no. 5, 4499-4549 (with P. Howard) arXiv:1603.02648

  8. The Morse and Maslov Indices for Schr\"odinger Operators, to appear in Journal d'Analyse Mathematique (with Y. Latushkin, S. Sukhtaiev) arXiv:1411.1656

  9. The Morse and Maslov indices for multidimensional Schr\"odinger operators with matrix-valued potentials, Trans. Amer. Math. Soc. 368 (2016), no. 11, 8145--8207
    (with G. Cox, C. Jones, Y. Latushkin) arXiv:1408.1103

  10. Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields, Nonlinearity 28 (2015), 577--592
    (with G. Berkolaiko, A. Comech) arXiv:1306.5150

  11. Thesis: "The Evans function, the Weyl-Titchmarsh function, and the Birman-Schwinger operators", July 2012

  12. The Evans function and the Weyl-Titchmarsh function, in Special issue on stability of travelling waves, Disc. Cont. Dynam. Syst. Ser. S 5 (2012), no. 5, 939 - 970 (with Y. Latushkin)

  13. The algebraic multiplicity of eigenvalues and the Evans function revisited, in Memorial M. Birman's volume, Mat. Model. Nat. Phenom., 5 (2010) 269 - 292 (with Y. Latushkin)

  14. Spectral decomposition of normal operators in Hilbert quaternion bimodules, Scientific Notes of Taurida National University, 19(58) (2006), no. 1, 3-20 (with I. Karpenko, D. Tyshkevich)

  15. On an approach to differentiation of functions of a quaternion variable, Scientific Notes of Taurida National University}, 17(56) (2004), no. 1, 30-37 (with I. Karpenko, D. Tyshkevich)