ACADEMY OF SCIENCES OF UKRAINE
INSTITUTE OF GEOPHYSICS

Division of Geodynamics of Explosion

Institute of Geophysics NAS of Ukraine


Vyacheslav Vakhnenko

Vyacheslav Vakhnenko
Position: Chief Scientist

Bogdan Khmelnytzky str. 63B, Kyiv, 01054, Ukraine
Tel: 380 (44) 234-14-60 (work),
380 (44) 526-14-59 (home)
Fax: 380 (44) 450-25-20
e-mail: vakhnenko@ukr.net

List of main publications

  1. V.O. Vakhnenko, E.J. Parkes, The inverse problem for some special spectral data, Chaos, Solitons and Fractals. 2016, v.82, 116-124.
  2. V.O. Vakhnenko, E.J. Parkes, Approach in Theory of Nonlinear Evolution Equations: The Vakhnenko-Parkes Equation, Advances in Mathematical Physics, v.2016, Article ID 2916582, 39 p. http://dx.doi.org/10.1155/2016/2916582
  3. V.O. Vakhnenko, Wave Dynamics of the Structured Media with Relaxation, Lap Lambert Academic Publishing, OmniScriptum GmbH & Co. KG, Saarbrucken, Germany. - 2015. - 173 p. ISBN: 978-3-659-68076-2
  4. O.O. Vakhnenko, V.O. Vakhnenko, Low-amplitude instability as a premise for the spontaneous symmetry breaking in the new integrable semidiscrete nonlinear system, Chaos, Solitons and Fractals. 2014, v.60, 1-10.
  5. O.O. Vakhnenko, V.O. Vakhnenko, Linear analysis of extended integrable nonlinear Ladder network system // Ukr. J. Phys. 2014, v. 59, No. 6, 640-649.
  6. V.O. Vakhnenko, Blast Waves in Multi-Component Medium with Thermal Relaxation, Natural Science, 2014, v. 6, 1055-1092.
  7. V.O Vakhnenko, E.J Parkes, The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method, Chaos, Solitons and Fractals, v.45, 846-852 (2012).
  8. V.O. Vakhnenko, E.J. Parkes, Solutions Associated with Discrete and Continuous Spectrums in the Inverse Scattering Method for the Vakhnenko-Parkes Equation, Progress of Theoretical Physics, v.127, No.4, 593-613, (2012).
  9. V.O. Vakhnenko, E.J. Parkes, Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations, J. Math. Phys., v.53, No.6, 063504(pages11) 2012.
  10. V.O. Vakhnenko, Special form of the singularity function for continuous part of the spectral data in inverse scattering method, Ukr. J. Phys., v.57, No.1, 95-99 (2012).
  11. V.O. Vakhnenko, Similarity in stationary motions of gas and two-phase medium with incompressible component, Intern. J. Non-Linear Mech., v.46, 1356-1360 (2011).
  12. V.O. Vakhnenko, Modeling of hysteretic behavior for sandstone under slow cyclic loading, Ukr. Geophys. J., v.33, No.4, 153-158 (2011) (in Ukrainian).
  13. V.O. Vakhnenko, Applying the inverse scattering transform method to the Vakhnenko-Parkes equation to describe the interaction of a soliton and a periodic wave, Rep.NAS Ukr., No.8, 73-79 (2011) (in Ukrainian).
  14. V.O. Vakhnenko, E.J. Parkes, Solutions associated with both the bound state spectrum and the special singularity function for continuous spectrum in inverse scattering method, Proceeding of School of Mechanics and Mathematics, V.N.Karazin Kharkov National University. In: Contemporary problems of mathematics, mechanics and computing sciences. N. N. Kizilova, G. N. Zholtkevych (eds.). - Kharkov: Publishing house PPB Virovec' A. P. Publishing house is a group 'Apostrophe', 2011, p. 364-376.
  15. V.Vakhnenko, O. Vakhnenko, J. TenCate, T. Shankland, Modeling of the nonlinear resonant response in sedimantary rocks, Ukr. Geophys. J., v.32, No.4, 195-197 (2010) (in English).
  16. V.O. Vakhnenko, An analogy of the self-similar flows of a gas and a two-phase medium with noncompressive component, Rep.NAS Ukr. No.12, 97-104 (2010) (in Ukrainian).
  17. V.O. Vakhnenko, O.O. Vakhnenko, J.A. TenCate, T.J. Shankland, Quasistatic loading of Berea sandstone, Rep.NAS Ukr. No1, 118-126 (2008).
  18. V.O. Vakhnenko, O.O. Vakhnenko, J.A. TenCate, T.J. Shankland, The dynamics of a sandstone bar under resonance loading, in Proceeding of the XX Session RAS, (27-31 October, 2008, Moscow).
  19. V.O. Vakhnenko, O.O. Vakhnenko, J. A. TenCate, T.J. Shankland, Modeling of stress-strain dependences for Berea sandstone under quasi-static loading, Phys. Rev. B, v.76, 184108(8pages) (2007).
  20. V.O.Vakhnenko, O.O.Vakhnenko, V.A.Danylenko, A relaxation model of the mechanical behaviour of a sandstone under quasistatic loading, Rep.NAS Ukr. N7, 109-115 (2007) (in Ukrainian).
  21. V.O. Vakhnenko, E. J. Parkes, The solutions of a generalized Degasperis-Procesi equation, Rep.NAS Ukr. No8, 88-94 (2006).
  22. O.O. Vakhnenko, V.O. Vakhnenko, T.J. Shankland, J.A. TenCate, Soft-ratchet modeling of slow dynamics in the nonlinear resonant response of sedimentary rocks, in Innovations in nonlinear acoustics: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum, AIP Conference Proceedings May 30, 2006 Volume 838, pp. 120-123.
  23. V.O. Vakhnenko, O.O. Vakhnenko, J.A. TenCate, T.J. Shankland, Dynamical realization of end-point memory in consolidated materials, in Innovations in nonlinear acoustics: ISNA17 - 17th International Symposium on Nonlinear Acoustics including the International Sonic Boom Forum, AIP Conference Proceedings May 30, 2006 Volume 838, pp. 124-127.
  24. E.J. Parkes, V.O. Vakhnenko, Explicit solutions of the CamassaHolm equation, Chaos, Solitons and Fractals, v 26, 13091316 (2005).
  25. O. Vakhnenko, V.O. Vakhnenko, and T.J. Shankland, Soft-ratchet modelling of end-point memory in the nonlinear resonant response of sedimentary rocks, Phys. Rev. B. v 71, 174103 (2005).
  26. O.O. Vakhnenko, V.O. Vakhnenko, T.J. Shankland, and J.A. Ten Cate, Strain-induced kinetics of intergrain defects as the mechanism of slow dynamics in the nonlinear resonant response of humid sandstone bars, Phys Rev E. 70, Repid communication, 015602(R) (2004).
  27. V.O. Vakhnenko, E.J. Parkes, Periodic and solitary-wave solutions of the Degasperis-Procesi equation, Chaos, Solitons and Fractals, v. 20, 1059-1073 (2004).
  28. V.O. Vakhnenko, E.J. Parkes, The Connection of the Degasperis-Procesi equation with the Vakhnenko equation, in Proceedinds of the Fifth International Conference Symmetry in Nonlinear Mathematical Physics, (23-29 June, 2003, Kyiv), Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych, Kyiv, Insitute of Mathematics, v.50, Part 1, 493-497 (2004).
  29. V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, A Backlund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos, Solitons and Fractals v. 17, 683 692 (2003).
  30. Vakhnenko V., Danylenko V. Nonlinear waves as a technical tool for diagnostics of the medium structure, Proceeding of the Tenth International Congress on Sound and Vibration (7-10 July, 2003, Stokholm, Sweden), 2003, v. 6, 3549-56.
  31. Mykulyak S., Vakhnenko V., Danylenko V. The wave spectral evolution in a discrete medium with nonlinearity, Proceeding of the Tenth International Congress on Sound and Vibration (7-10 July, 2003, Stokholm, Sweden), 2003, Vol. 6, 3573-9.
  32. V.. Vkhnenko, V.P. Ngorny, I.I. Denisyuk, and .V. Mishchenko, Estimation of rock failure zone under confined explosion, Journal of Mining Science, v. 39, No. 3, 247-254 (2003).
  33. V.O. Vakhnenko, E.J. Parkes, The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method, Chaos, Solitons and Fractals vol. 13/9 1819-1826 (2002).
  34. V.O. Vakhnenko, E.J. Parkes, The Inverse Scattering Method for the Equation Describing the High-Frequency Waves in a Relaxing Medium, in Nonlinear Acoustics at the Beginning of the 21st Century, eds. O.V. Rudenko and O.A. Sapozhnikov (Faculty of Physics, MSU, Moscow, 2002) vol. 1, pp. 121-124.
  35. V.O. Vakhnenko, Diagnostics of the Medium Structure by Long Nonlinear Wave, in in Nonlinear Acoustics at the Beginning of the 21st Century, eds. O.V. Rudenko and O.A. Sapozhnikov (Faculty of Physics, MSU, Moscow, 2002) vol. 1, pp. 847-850.
  36. V.O. Vakhnenko, E.J. Parkes, A novel nonlinear evolution equation integrable by the inverse scattering method, in Proceedinds of Fourth International Conference Symmetry in Nonlinear Mathematical Physics (9-15 July, 2001, Kyiv), Editors A.G. Nikitin, V.M. Boyko and R.O. Popovych, Kyiv, Insitute of Mathematics, 2002, v.43, Part 1, 384-91.
  37. V. O. Vakhnenko, E. J. Parkes, A novel nonlinear evolution equation and its Backlund transformation, Rep.NAS Ukr. N6, 9196 (2001) (In English).
  38. V.O. Vakhnenko, E.J. Parkes, A.J. Morrison, Integrability of a novel nonlinear evolution equation, Rep.NAS Ukr. N6, 8692 (2002).
  39. V.O. Vakhnenko, E.J. Parkes, A novel nonlinear evolution equation integrable by the inverse scattering method, Rep.NAS Ukr. N7, 81-86 (2001).
  40. V.O. Vakhnenko, V.A. Danylenko, A.V. Michtchenko, Diagnostics of the medium structure by long wave of finite amplitude, Inter. J. Non-Linear Mech., 2000, v.35, p.1105-1113.
  41. V.O. Vakhnenko, E.J. Parkes, A.V. Michtchenko, The Vakhnenko equation from the viewpoint of the inverse scattering method for the KdV equation, Inter. J. Differ. Eq. Appl., 2000, v.1, N4, p.429-450.
  42. A.J. Morrison, E.J.,Parkes, V.O. Vakhnenko, The N loop soliton solution of the Vakhnenko equation, Nonlinearity, 1999, v.12, p. 1427-1437.
  43. V.O. Vakhnenko, E.J. Parkes, V.A. Danylenko, Exact two-soliton solutions of a model nonlinear equation, Ukrainian Journal of Physics, 1999, v.44, N6, p.782-790 (in Ukrainian).
  44. V.O. Vakhnenko, High frequency soliton-like waves in a relaxing medium, J. Math. Phys., 1999, v.40, N3, p.2011-2020.
  45. V.A. Vakhnenko, Increase of nonlinear effect in a medium with microstructure, Acoustical Physics, 1999, v. 45, N2, p.151-157.
  46. V.O. Vakhnenko, V.A. Danylenko, A.V. Michtchenko, An asymptotic averaged model of nonlinear long waves propagation in media with a regular structure, Inter. J. Non-Linear Mech., 1999, v.34, p.643-654.
  47. V.O. Vakhnenko, E.J. Parkes, The two loop soliton solution of the Vakhnenko equation, Nonlinearity, 1998, v.11, p.1457-1464.
  48. V.O. Vakhnenko, The existence of loop-like solutions of a model evolution equation, Ukrainian Journal of Physics, (in Ukrainian), 1997, v.42, N1, p.104-110.)
  49. V.A. Vakhnenko, Diagnosis of the properties of a structurized medium by long nonlinear waves, Journal of Applied Mechanics and Technical Physics, 1996, v.37, N5, 643-649.
  50. V.A. Vakhnenko, V.A. Danylenko, An asymptotic model of non-linear waves in natural multi-component media, Geophys. J., 1997, v.16, p. 674-685.
  51. V.A. Vakhnenko, V.A. Danylenko, V.V. Kulich, Asymptotic justification of the Lyakhov model for multicomponent media, Combustion, Explosion and Shock Waves, 1996, v.32, N2, p.176-180.
  52. O.O. Vakhnenko, V.O. Vakhnenko, Physically corrected Ablowitz-Ladik model and its application to the Peierls-Nabarro problem, Phys.Letters A, 1995, v.196, N5-6, p.307-312.
  53. V.A. Vakhnenko, V.A.Danilenko, V.V.Kulich, Averaged description of shock-wave processes in periodic media, Sov.J.Chem.Phys., 1994, v.12(3), p.534-546.
  54. V.A. Vakhnenko, V.A. Danilenko, V.V. Kulich, Averaged description of wave processes in geophysical medium, Geophysics J., (Ukraine), 1993, v.15, N6, p.66-71.
  55. V.A. Vakhnenko, Solitons in a nonlinear model medium, J.Phys.A: Math.Gen., 1992, v.26, N15, p.4181-4187.
  56. V.A. Vakhnenko and V.V. Kulich, Long-wave processes in periodic media, J.Appl. Mech. and Techn. Phys., 1992, v.32, p.814-820.
  57. V.A. Vakhnenko, Periodic short-wave perturbations in a relaxing medium, Preprint, Institute of Geophysics, Ukrainian Acad. Sci., Kiev, 1991, 20p. (in Russian).
  58. V.A. Vakhnenko, V.A. Danilenko, V.V. Kulich, Wave processes in periodic relaxing medium, Doklady Akademii nauk Ukrainskoi SSR 1991, N4, p.93-96.
  59. V.M. Kudinov, B.I. Palamarchuk and V.A. Vakhnenko, Analysis of shock wave, Sov. Phys. Dokl. v. 28(10), October 1983, p.842-843.
  60. V.A. Vakhnenko, B.A. Kurchj, Resonance model of lodging, Physiology and biochemistry of cultivated plants, 1990, v.22, N3, p.245-252.
  61. L.S. Brizhik, Yu.B. Gaididei, A.A. Vakhnenko, V.A. Vakhnenko, Solitons generation in semi-infinite molecular chains, Physics stat.sol (b), 1988, v.146, N2, p.606-612.
  62. A.V. Gayek, E.G. Popov, V.A. Vakhnenko, V.N. Bykov, B.I. Palamarchuk, Explosion parameters of oxyhydrocarbon mixtures in closed volume at explosive working, Fizika i khimija obrabotki materialov, 1988, N5, p.37-42.
  63. V.A. Vakhnenko, B.A. Kurchj, Physical-mathematical model of lodging, Doklady Akademii nauk Ukr.SSR B, 1988, N12, p.54-56.
  64. V.A. Vakhnenko, B.I. Palamarchuk, Evolution of strong shock waves in a medium with thermal relaxation, Soviet Applied Mechanics, 1986, September, p.267-277.
  65. V.A. Vakhnenko and B.I. Palamarchuk, Description of shock-wave processes in a two-phase mrdium containing an incompressible phase, Journal of Applied Mechanics and Technical Physics, 1984, N1, p. 101-107.
  66. V.A.Vakhnenko, V.M. Kudinov and B.I. Palamarchuk, Damping of srtong shocks in relaxing media, Combustion, Explosion and Shock Waves, 1984, v. 20, N1, p. 97--103.
  67. V.A. Vakhnenko, I.A. Izmailov, V.A. Kochelap, Recombination gasdynamic lasers on electron transitions in diatomic molecules. Ukrainian Journal of Physics, 1984, v.29, N7, p. 996-1002.
  68. V.M. Kudinov, B.I. Palamarchuk, V.A. Vakhnenko, A.V. Cherkashin, S.G. Lebed, A.T. Malakhov, Relaxation phenomena in two-phase media of a foamy structure. In: Shock Waves, Explosion, and Detonations. New York: AIAA, 1983, p. 96-118.
  69. V.A. Vakhnenko, V.M. Kudinov, B.I. Palamarchuk, Effect of thermal relaxation on attenuation of shock waves in two-phase medium, Soviet Applied Mechanics, 1983, June, p. 1126-1133.
  70. V.A. Vakhnenko, V.M. Kudinov, B.I. Palamarchuk, Analogy of motion of the two-phase media containing incompressible and gaseous phases with gas motion, Doklady Akademii nauk Ukr.SSR A, 1983, N6, p. 22-24.
  71. N.Ya. Vasilik, V.A. Vakhnenko, A.D. Margolin, V.M. Shmelev. Energy characteristics of a carbon monoxide gasdynamics laser. Journal of Applied Mechanics and Technical Physics, 1978, N5, p. 587-593.

Last modified in March 2016
e-mail: vakhnenko@ukr.net