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John Parkes MA, MMath, PhD (Cantab)

Position: Honorary Research Fellow (as from 1 October 2011; formerly Senior Lecturer)

Department of Mathematics & Statistics
University of Strathclyde
Livingstone Tower
Richmond Street
Glasgow, G1 1XH,
U.K.

Telephone: +44 141 548 3804

Mobile: +44 7929 018488

E-mail: e.j.parkes@strath.ac.uk

Research Interests

Research Papers

  1. Parkes, E. J., The ray tracing treatment of the oblique echo model for the topside upper hybrid resonance, Journal of Plasma Physics 12 (1974), 107-127.
  2. Parkes, E. J., An analytical study of the oblique echo model for the topside plasma resonance, Journal of Plasma Physics 12 (1974), 199-216.
  3. Parkes, E. J., An analytical study of the oblique echo model for the topside upper hybrid resonance, Journal of Plasma Physics 12 (1974), 217-232.
  4. Gribben, R. J. & Parkes, E. J., Slowly varying nonlinear waves in a cold plasma stream, Journal of Plasma Physics 18 (1977), 495-508.
  5. Parkes, E. J. & Gribben, R. J., A note on the application of the method of strained coordinates to a problem of wave propagation in plasmas, Journal of Physics A: Math. Gen. 11 (1978), 2341-2348.
  6. Gribben, R. J. & Parkes, E. J., Slowly varying nonlinear waves in a warm plasma stream, Journal of Physics A: Math. Gen. 14 (1981), 2113-2119.
  7. Parkes, E. J., The modulation of nonlinear dispersive waves in a warm plasma stream, Journal of Physics A: Math. Gen. 15 (1982), 1425-1430.
  8. Parkes, E. J., The modulation of weakly nonlinear dispersive waves near the marginal state of instability, Journal of Physics A: Math. Gen. 20 (1987), 2025-2036.
  9. Parkes, E. J., The modulation of weakly nonlinear ion acoustic plasma waves near the marginal state of instability, Journal of Physics A: Math. Gen. 20 (1987), 3653-3666.
  10. Parkes, E. J., Nonlinear wave modulation near the marginal state of instability, Journal of Physics A: Math. Gen. 21 (1988), 2533-2546.
  11. Parkes, E. J., The modulation instability of the nonlinear Klein-Gordon equation, Wave Motion 13 (1991), 261-275.
  12. Parkes, E. J., The influence of ion streaming and weak relativistic effects on the modulational instability of ion acoustic waves, Journal of Plasma Physics 48 (1992), 477-486.
  13. Parkes, E. J., The influence of electron inertia on the modulational instability of ion acoustic waves, Journal of Plasma Physics 49 (1993), 395-402.
  14. Parkes, E. J., The stability of solutions of Vakhnenko’s equation, Journal of Physics A: Math. Gen. 26 (1993), 6469-6475.
  15. Parkes, E. J., Exact solutions to the two-dimensional Korteweg-de Vries-Burgers equation, Journal of Physics A: Math. Gen. 27 (1994), L497-L501.
  16. Duffy, B. R. & Parkes, E. J., Travelling solitary wave solutions to a seventh-order generalised KdV equation, Physics Letters A 214 (1996), 271-272.
  17. Parkes, E. J. & Duffy, B. R., An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Computer Physics Communications 98 (1996), 288-300.
  18. O'Keir, I. S. & Parkes, E. J., The derivation of a modified Kadomtsev-Petviashvili equation and the stability of its solutions, Physica Scripta 55 (1997), 135-142.
  19. Parkes, E. J. & Duffy, B. R., Travelling solitary wave solutions to a compound KdV-Burgers equation, Physics Letters A 229 (1997), 217-220.
  20. Parkes, E. J., Zhu, Z., Duffy, B. R. & Huang, H. C., Sech-polynomial travelling solitary-wave solutions of odd-order generalized KdV equations, Physics Letters A 248 (1998), 219-224.
  21. Vakhnenko, V. O. & Parkes, E. J., The two loop soliton solution of the Vakhnenko equation, Nonlinearity 11 (1998), 1457-1464.
  22. Vakhnenko, V. O., Parkes, E. J. & Danylenko, V. A., Exact two-soliton solutions of a model evolution equation, Ukrainian Journal of Physics 44 (1999), 782-790.
  23. Morrison, A. J., Parkes, E. J. & Vakhnenko, V. O., The N loop soliton solution of the Vakhnenko equation, Nonlinearity 12 (1999), 1427-1437.
  24. Munro, S. & Parkes, E. J., The derivation of a modified Zakharov-Kuznetsov equation and the stability of its solutions, Journal of Plasma Physics 62 (1999), 305-317.
  25. Vakhnenko, V. O., Parkes, E. J. & Michtchenko, A. V., The Vakhnenko equation from the viewpoint of the inverse scattering method for the KdV equation, International Journal of Differential Equations and Applications 1 (2000), 429-449.
  26. Munro, S. & Parkes, E. J., The stability of solitary-wave solutions to a modified Zakharov-Kuznetsov equation, Journal of Plasma Physics 64 (2000), 411-426.
  27. Morrison, A. J. & Parkes, E. J., The N-soliton solution of a generalised Vakhnenko equation, Glasgow Mathematical Journal 43A (2001), 65-90.
  28. Vakhnenko, V. O. & Parkes, E. J., A novel nonlinear evolution equation and its Bäcklund transformation, Rep. NAS Ukr. N6 (2001), 91-96.
  29. Vakhnenko, V. O. & Parkes, E. J., The calculation of multi-soliton solutions of the Vakhnenko equation by the inverse scattering method, Chaos, Solitons & Fractals 13 (2002), 1819-1826.
  30. Parkes, E. J., Duffy, B. R. & Abbott, P. C., The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations, Physics Letters A 295 (2002), 280-286.
  31. Vakhnenko, V. O., Parkes, E. J. & Morrison, A. J., Integrability of a novel nonlinear evolution equation, Rep. NAS Ukr. N6 (2002), 86-92.
  32. Morrison, A. J. & Parkes, E. J., The N-soliton solution of the modified generalised Vakhnenko equation (a new nonlinear evolution equation), Chaos, Solitons & Fractals 16 (2003), 13-26.
  33. Vakhnenko, V. O., Parkes, E. J. & Morrison, A. J., A Bäcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos, Solitons & Fractals 17 (2003), 683-692.
  34. Parkes, E. J., A note on Demiray’s solution to the perturbed Burger’s equation, Applied Mathematical Modelling 27 (2003), 487-488.
  35. Parkes, E. J., A note on solitary-wave solutions to compound KdV-Burgers equations, Physics Letters A 317 (2003), 424-428.
  36. Wen-Shan Duan & John Parkes, Dust size distribution for dust acoustic waves in a magnetized dusty plasma, Physical Review E 68 (2003), 067402.1-067402.4.
  37. Vakhnenko, V. O. & Parkes, E. J., Periodic and solitary-wave solutions of the Degasperis-Procesi equation, Chaos, Solitons & Fractals 20 (2004), 1059-1073.
  38. Wen-Shan Duan, John Parkes & Lei Zhang, Modulational instability of dust envelope waves with grain and charge distribution, Physics of Plasmas 11 (2004), 3762-3766.
  39. Munro, S. & Parkes, E. J., The stability of obliquely-propagating solitary-wave solutions to a modified Zakharov-Kuznetsov equation, Journal of Plasma Physics 70 (2004), 543-552.
  40. Duan, W-S., Parkes, J. & Lin, M-M., Wave packet in a two-dimensional hexagonal crystal, Physics of Plasmas 12 (2005), 022106.
  41. Parkes, E. J. & Munro, S., The stability of obliquely-propagating solitary-wave solutions to Zakharov-Kuznetsov type equations, Journal of Plasma Physics 71 (2005), 695-708.
  42. Parkes, E. J. & Vakhnenko, V. O., Explicit solutions of the Camassa-Holm equation, Chaos, Solitons & Fractals 26 (2005), 1309-1316.
  43. Duan, W-S., Wang, H-Y. & Parkes, J., Compressive and rarefactive waves in dust plasma with non-thermal ions, Communications in Theoretical Physics 45 (2006), 1112-1116.
  44. Vakhnenko, V. O. & Parkes, E. J., The solutions of a generalized Degasperis-Procesi equation, Rep. NAS Ukr. N8 (2006), 88-94.
  45. Parkes, E. J., Explicit solutions of the reduced Ostrovsky equation, Chaos, Solitons & Fractals 31 (2007), 602-610.
  46. Abbasbandy, S. & Parkes, E. J., Solitary smooth hump solutions of the Camassa-Holm equation by means of the homotopy analysis method, Chaos, Solitons & Fractals 36 (2008), 581-591.
  47. Parkes, E. J., Some periodic and solitary travelling-wave solutions of the short-pulse equation, Chaos, Solitons & Fractals 38 (2008), 154-159.
  48. Parkes, E. J., Periodic and solitary travelling-wave solutions of an extended reduced Ostrovsky equation, SIGMA 4 (2008), 053, 17 pages; arXiv:0806.3155.
  49. Parkes, E. J. & Abbasbandy, S., Finding the one-loop soliton solution of the short-pulse equation by means of the homotopy analysis method, Numerical Methods for Partial Differential Equations 25 (2009), 401-408.
  50. Parkes, E. J., A note on travelling-wave solutions to Lax’s seventh-order KdV equation, Applied Mathematics & Computation 215 (2009), 864-865.
  51. Parkes, E. J., A note on solitary travelling-wave solutions to the transformed reduced Ostrovsky equation, Communications in Nonlinear Science and Numerical Simulation 15 (2010), 2769-2771.
  52. Abbasbandy, S. & Parkes, E. J., Solitary-wave solutions of the Degasperis-Procesi equation by means of the homotopy analysis method, International Journal of Computer Mathematics 87 (2010), 2303-2313.
  53. Parkes, E. J., A note on loop-soliton solutions of the short-pulse equation, Physics Letters A 374 (2010), 4321-4323.
  54. Deng, X., Parkes, E. J. & Cao, J., Exact solitary and periodic-wave solutions of the K(2,2) equation (defocusing branch), Applied Mathematics & Computation 217 (2010), 1566-1576.
  55. Parkes, E. J., Observations on the tanh-coth expansion method for finding solutions to nonlinear evolution equations, Applied Mathematics & Computation 217 (2010), 1749-1754.
  56. Parkes, E. J., Observations on the basic G'/G-expansion method for finding solutions to nonlinear evolution equations, Applied Mathematics & Computation 217 (2010), 1759-1763.
  57. Parkes, E. J., A note on "New travelling wave solutions to the Ostrovsky equation", Applied Mathematics & Computation 217 (2010), 3575-3577.
  58. Parkes, E. J., Comment on "Application of (G'/G)-expansion method to travelling wave solutions of three nonlinear evolution equation" [Computers & Fluids 2010;39:1957-1963], Computers & Fluids 42 (2011), 108-109.
  59. Vakhnenko, V. O. & Parkes, E. J., Solutions associated with discrete and continuous spectrums in the inverse scattering method for the Vakhnenko-Parkes equation, Progress of Theoretical Physics 127 (2012), 593-613.
  60. Vakhnenko, V. O. & Parkes, E. J., The singular solutions of a nonlinear evolution equation taking continuous part of the spectral data into account in inverse scattering method, Chaos, Solitons & Fractals 45 (2012), 846-852.
  61. Vakhnenko, V. O. & Parkes, E. J., Special singularity function for continuous part of the spectral data in the associated eigenvalue problem for nonlinear equations, Journal of Mathematical Physics 53 (2012), 063504.

Recent Departmental Research Reports

  1. Parkes, E. J., Comments on the use of the tanh-coth expansion method for finding solutions to nonlinear evolution equations , Research Report No. 33 (2009).

Conference Proceedings

  1. Parkes, E.J., 1980 Propagation of slowly varying nonlinear waves in plasmas II: Cold and warm plasma streams, in Mathematical Methods of Plasma Physics, ed. R. Kress & J. Wick (Peter D. Lang, Frankfurt) pp. 37-49.
  2. Parkes, E.J. 1995 Solitary ion-acoustic waves in a plasma with negative ions and non-isothermal electrons, Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology, Heriot-Watt University} ed. D.B. Duncan & J.C. Eilbeck, published electronically.
  3. Fiona Campbell & John Parkes, The internal structure of the two-soliton solution to nonlinear evolution equations of a certain class, SOLPHYS 1997, Technical University of Denmark, published electronically.
  4. Susan Munro & John Parkes, The stability of solitary wave solutions to a modified Zakharov-Kuznetsov equation, SOLPHYS 1997, Technical University of Denmark, published electronically.
  5. Vakhnenko, V. O. & Parkes, E. J., A novel nonlinear evolution equation integrable by the inverse scattering method, Proceedings of the Fourth International Conference on Symmetry in Nonlinear Mathematical Physics, Kyiv 2001, published in Proceedings of the Institute of Mathematics of NAS of Ukraine 43 (2002), 384-391.
  6. Vakhnenko, V. O. & Parkes, E. J., The inverse scattering method for the equation describing high-frequency waves in a relaxing medium, Proceedings of the 16th International Symposium on Nonlinear Acoustics, Moscow, 2002, published in Nonlinear Acoustics at the Beginning of the 21st Century, ed. O. V. Rudenko & O. A. Sapozhnikov, Faculty of Physics, MSU, Moscow, 2002. Volume 1, 121-124.
  7. Vakhnenko, V. O. & Parkes, E. J., The connection of the Degasperis-Procesi equation with the Vakhnenko equation, Proceedings of the Fifth International Conference on Symmetry in Nonlinear Mathematical Physics, Kyiv 2003, published in Proceedings of the Institute of Mathematics of NAS of Ukraine 50 (2004), 493-497.

Book Reviews

  1. Parkes, E.J., Solitary waves in plasmas and in the atmosphere, by V.I. Petviashvili & O.A. Pokhotelov (Gordon & Breach, Reading), Plasma Physics and Controlled Fusion 35 (1993), 128-129.
  2. Parkes, E.J., The direct method in soliton theory, by R. Hirota (Cambridge University Press), Proceedings of the Edinburgh Mathematical Society 50 (2007), 252-253.

Other Interests


Last modified in October 2012
e.j.parkes@strath.ac.uk