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

Email: e.j.parkes@strath.ac.uk

 Loop solitons and other exotic solutions to nonlinear evolution equations
 Methods for finding solitarywave and periodicwave
solutions to nonlinear evolution equations
 Stability of fully nonlinear waves in dispersive media
 Internal dynamics of soliton interactions
 Weakly nonlinear wave propagation in dispersive media
Research Papers
 Parkes, E. J.,
The ray tracing treatment of the oblique
echo model for the topside upper hybrid resonance,
Journal of Plasma Physics 12 (1974), 107127.
 Parkes, E. J.,
An analytical study of the oblique echo
model for the topside plasma resonance,
Journal of Plasma Physics 12 (1974), 199216.
 Parkes, E. J.,
An analytical study of the oblique echo
model for the topside upper hybrid resonance,
Journal of Plasma Physics 12 (1974), 217232.
 Gribben, R. J. & Parkes, E. J.,
Slowly varying nonlinear waves in a cold plasma stream,
Journal of Plasma Physics 18 (1977), 495508.
 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), 23412348.
 Gribben, R. J. & Parkes, E. J.,
Slowly varying nonlinear waves in a warm plasma stream,
Journal of Physics A: Math. Gen. 14 (1981), 21132119.
 Parkes, E. J.,
The modulation of nonlinear dispersive waves in a warm plasma stream,
Journal of Physics A: Math. Gen. 15 (1982), 14251430.
 Parkes, E. J.,
The modulation of weakly nonlinear dispersive waves
near the marginal state of instability,
Journal of Physics A: Math. Gen. 20 (1987), 20252036.
 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), 36533666.
 Parkes, E. J.,
Nonlinear wave modulation near the marginal state of instability,
Journal of Physics A: Math. Gen. 21 (1988), 25332546.
 Parkes, E. J.,
The modulation instability of the nonlinear KleinGordon equation,
Wave Motion 13 (1991), 261275.
 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), 477486.
 Parkes, E. J.,
The influence of electron inertia on the
modulational instability of ion acoustic waves,
Journal of Plasma Physics 49 (1993), 395402.
 Parkes, E. J.,
The stability of solutions of Vakhnenko’s equation,
Journal of Physics A: Math. Gen. 26 (1993), 64696475.
 Parkes, E. J.,
Exact solutions to the twodimensional Kortewegde VriesBurgers equation,
Journal of Physics A: Math. Gen. 27 (1994), L497L501.
 Duffy, B. R. & Parkes, E. J.,
Travelling solitary wave solutions to a seventhorder generalised KdV equation,
Physics Letters A 214 (1996), 271272.
 Parkes, E. J. & Duffy, B. R.,
An automated tanhfunction method for finding solitary wave solutions to nonlinear
evolution equations,
Computer Physics Communications 98 (1996), 288300.
 O'Keir, I. S. & Parkes, E. J.,
The derivation of a modified KadomtsevPetviashvili equation and
the stability of its solutions,
Physica Scripta 55 (1997), 135142.
 Parkes, E. J. & Duffy, B. R.,
Travelling solitary wave solutions to a compound KdVBurgers equation,
Physics Letters A 229 (1997), 217220.
 Parkes, E. J., Zhu, Z., Duffy, B. R. & Huang, H. C.,
Sechpolynomial travelling solitarywave solutions of
oddorder generalized KdV equations,
Physics Letters A 248 (1998), 219224.
 Vakhnenko, V. O. & Parkes, E. J.,
The two loop soliton solution of the Vakhnenko equation,
Nonlinearity 11 (1998), 14571464.
 Vakhnenko, V. O., Parkes, E. J. & Danylenko, V. A.,
Exact twosoliton solutions of a model evolution equation,
Ukrainian Journal of Physics 44 (1999), 782790.
 Morrison, A. J., Parkes, E. J. & Vakhnenko, V. O.,
The N loop soliton solution of the Vakhnenko equation,
Nonlinearity 12 (1999), 14271437.
 Munro, S. & Parkes, E. J.,
The derivation of a modified ZakharovKuznetsov equation and
the stability of its solutions,
Journal of Plasma Physics 62 (1999), 305317.
 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), 429449.
 Munro, S. & Parkes, E. J.,
The stability of solitarywave solutions to a modified
ZakharovKuznetsov equation,
Journal of Plasma Physics 64 (2000), 411426.
 Morrison, A. J. & Parkes, E. J.,
The Nsoliton solution of a generalised Vakhnenko equation,
Glasgow Mathematical Journal 43A (2001), 6590.
 Vakhnenko, V. O. & Parkes, E. J.,
A novel nonlinear evolution equation and its Bäcklund transformation,
Rep. NAS Ukr. N6 (2001), 9196.
 Vakhnenko, V. O. & Parkes, E. J.,
The calculation of multisoliton solutions of the Vakhnenko
equation by the inverse scattering method,
Chaos, Solitons & Fractals 13 (2002), 18191826.
 Parkes, E. J., Duffy, B. R. & Abbott, P. C.,
The Jacobi ellipticfunction method for finding periodicwave
solutions to nonlinear evolution equations,
Physics Letters A 295 (2002), 280286.
 Vakhnenko, V. O., Parkes, E. J. & Morrison, A. J.,
Integrability of a novel nonlinear evolution equation,
Rep. NAS Ukr. N6 (2002), 8692.
 Morrison, A. J. & Parkes, E. J.,
The Nsoliton solution of the modified generalised Vakhnenko
equation (a new nonlinear evolution equation),
Chaos, Solitons & Fractals 16 (2003), 1326.
 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), 683692.
 Parkes, E. J.,
A note on Demiray’s solution to the perturbed Burger’s
equation,
Applied Mathematical Modelling 27 (2003), 487488.
 Parkes, E. J.,
A note on solitarywave solutions to compound KdVBurgers
equations,
Physics Letters A 317 (2003), 424428.
 WenShan Duan & John Parkes,
Dust size distribution for dust acoustic waves in a
magnetized dusty plasma,
Physical Review E 68 (2003),
067402.1067402.4.
 Vakhnenko, V. O. & Parkes, E. J.,
Periodic and solitarywave solutions of the DegasperisProcesi equation,
Chaos, Solitons & Fractals 20 (2004), 10591073.
 WenShan Duan, John Parkes & Lei Zhang,
Modulational instability of dust envelope waves with grain and
charge distribution,
Physics of Plasmas 11 (2004), 37623766.
 Munro, S. & Parkes, E. J.,
The stability of obliquelypropagating solitarywave solutions to
a modified ZakharovKuznetsov equation,
Journal of Plasma Physics 70 (2004), 543552.
 Duan, WS., Parkes, J. & Lin, MM.,
Wave packet in a twodimensional hexagonal crystal,
Physics of Plasmas 12 (2005), 022106.
 Parkes, E. J. & Munro, S.,
The stability of obliquelypropagating solitarywave solutions to
ZakharovKuznetsov type equations,
Journal of Plasma Physics 71 (2005), 695708.
 Parkes, E. J. & Vakhnenko, V. O.,
Explicit solutions of the CamassaHolm equation,
Chaos, Solitons & Fractals 26 (2005), 13091316.
 Duan, WS., Wang, HY. & Parkes, J.,
Compressive and rarefactive waves in dust plasma with nonthermal ions,
Communications in Theoretical Physics 45 (2006), 11121116.
 Vakhnenko, V. O. & Parkes, E. J.,
The solutions of a generalized DegasperisProcesi equation,
Rep. NAS Ukr. N8 (2006), 8894.
 Parkes, E. J.,
Explicit solutions of the reduced Ostrovsky equation,
Chaos, Solitons & Fractals 31 (2007), 602610.
 Abbasbandy, S. & Parkes, E. J.,
Solitary smooth hump solutions of the CamassaHolm equation by
means of the homotopy analysis method,
Chaos, Solitons & Fractals 36 (2008), 581591.
 Parkes, E. J.,
Some periodic and solitary travellingwave solutions of the
shortpulse equation,
Chaos, Solitons & Fractals 38 (2008), 154159.
 Parkes, E. J.,
Periodic and solitary travellingwave solutions of an extended reduced
Ostrovsky equation,
SIGMA 4 (2008), 053, 17 pages; arXiv:0806.3155.
 Parkes, E. J. & Abbasbandy, S.,
Finding the oneloop soliton solution of the shortpulse equation
by means of the homotopy analysis method,
Numerical Methods for Partial Differential Equations 25 (2009), 401408.
 Parkes, E. J.,
A note on travellingwave solutions to Lax’s seventhorder KdV equation,
Applied Mathematics & Computation 215 (2009), 864865.
 Parkes, E. J.,
A note on solitary travellingwave solutions to the transformed reduced Ostrovsky equation,
Communications in Nonlinear Science and Numerical Simulation 15 (2010), 27692771.
 Abbasbandy, S. & Parkes, E. J.,
Solitarywave solutions of the DegasperisProcesi equation by means
of the homotopy analysis method,
International Journal of Computer Mathematics 87 (2010), 23032313.
 Parkes, E. J.,
A note on loopsoliton solutions of the shortpulse equation,
Physics Letters A 374 (2010), 43214323.
 Deng, X., Parkes, E. J. & Cao, J.,
Exact solitary and periodicwave solutions of the K(2,2) equation (defocusing branch),
Applied Mathematics & Computation 217 (2010), 15661576.
 Parkes, E. J.,
Observations on the tanhcoth expansion method for finding solutions to
nonlinear evolution equations,
Applied Mathematics & Computation 217 (2010), 17491754.
 Parkes, E. J.,
Observations on the basic G'/Gexpansion method for finding solutions to
nonlinear evolution equations,
Applied Mathematics & Computation 217 (2010), 17591763.
 Parkes, E. J.,
A note on "New travelling wave solutions to the Ostrovsky equation",
Applied Mathematics & Computation 217 (2010), 35753577.
 Parkes, E. J.,
Comment on "Application of (G'/G)expansion method to travelling wave
solutions of three nonlinear evolution equation" [Computers & Fluids 2010;39:19571963],
Computers & Fluids 42 (2011), 108109.
 Vakhnenko, V. O. & Parkes, E. J.,
Solutions associated with discrete and continuous spectrums in the inverse scattering method
for the VakhnenkoParkes equation,
Progress of Theoretical Physics 127 (2012), 593613.
 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), 846852.
 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, 11 pages.
 Vakhnenko, V. O. & Parkes, E. J.,
Approach in theory of nonlinear evolution equations: the VakhnenkoParkes equation,
Advances in Mathematical Physics 2016 (2016), Article ID 2916582, 39 pages.
Recent Departmental Research Reports
 Parkes, E. J.,
Comments on the use of the tanhcoth expansion method for finding solutions to
nonlinear evolution equations ,
Research Report No. 33 (2009).
Conference Proceedings & Contributions to Edited Volumes
 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. 3749.
 Parkes, E.J. 1995
Solitary ionacoustic waves in a plasma with
negative ions and nonisothermal electrons,
Proceedings of the Conference on Nonlinear Coherent Structures in Physics and Biology, HeriotWatt
University} ed. D.B. Duncan & J.C. Eilbeck, published electronically.
 Fiona Campbell & John Parkes,
The internal structure of the twosoliton solution to
nonlinear evolution equations of a certain class,
SOLPHYS 1997, Technical University of
Denmark, published electronically.
 Susan Munro & John Parkes,
The stability of solitary wave solutions to a modified
ZakharovKuznetsov equation,
SOLPHYS 1997, Technical University of
Denmark, published electronically.
 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), 384391.
 Vakhnenko, V. O. & Parkes, E. J.,
The inverse scattering method for the equation describing
highfrequency 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, 121124.
 Vakhnenko, V. O. & Parkes, E. J.,
The connection of the DegasperisProcesi 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), 493497.
 Vakhnenko, V. O. & Parkes, E. J., 2011
Solutions associated with both the bound state spectrum and the special
singularity function for continuous spectrum in inverse scattering method,
in Contemporary Problems of Mathematics, Mechanics and Computing Sciences,
ed. N. N. Kizilova & G. N. Zholtkevych (Kharkov National University, Kharkov) pp. 364376.
Book Reviews
 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), 128129.
 Parkes, E.J.,
The direct method in soliton theory,
by R. Hirota (Cambridge University Press),
Proceedings of the Edinburgh Mathematical Society 50 (2007), 252253.
Last modified in March 2016
e.j.parkes@strath.ac.uk