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Gennady El: List of Publications |
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Book Chapter El, G.A., Korteweg -- de Vries equation: solitons and undular bores, in: Solitary Waves in Fluids, Advances in Fluid Mechanics v. 47, R.H.J. Grimshaw (ed), WIT Press (2007) pp. 19 - 53, ISBN: 1-84564-157-4, pdf Journal Papers Submitted El, G.A., Khodorovskii, V.V. and Leszczyszyn, A.M., Refraction of dispersive shock waves, arXiv:1105.1920
Published 2011
El, G.A.,
2010 Molokov, S., El, G. and Lukyanov, A., Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field, Theor Comput Fluid Dyn (2010) Online First DOI 10.1007/s00162-010-0201-y, pdf.
2009 El, G.A. and Grimshaw, R.H.J. and Smyth, N.F., Transcritical shallow-water flow past topography: finite-amplitude theory, Journ Fluid Mech 640 (2009) 187 - 214. pdf El, G.A., Kamchatnov, A.M., Khodorovskii, V.V., Annibale, E.S. and Gammal, A., Two-dimensional supersonic nonlinear Schrödinger flow past an extended obstacle, Phys Rev E 80 (2009) Art No 046317. pdf Leszczyszyn, A.M., El, G.A., Gladush, Yu.G. and Kamchatnov, A.M., Transcritical flow of a Bose-Einstein condensate through a penetrable barrier, Phys Rev A 79 (2009) Art No 063608. pdf Horng, T.-L.,. Gou, S.-C., Lin, T.-C., El, G.A., Itin, A.P., and Kamchatnov, A.M., Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate, Phys Rev A 79 (2009) Art No 053619. pdf
2008 Khamis, E.G., Gammal, A., El, G.A., Gladush, Yu.G., Kamchatnov, A.M., Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire, Phys Rev A 78 (2008) Art No 013829. pdf El, G.A., Grimshaw, R.H.J. and Smyth, N.F., Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory, Physica D 237 (2008) 2423 - 2435. pdf
El, G.A., Grimshaw R.H.J. and Kamchatnov, A.M., Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction, Journ Fluid Mech 585 (2007) 213 - 244. pdf El, G.A., Gladush, Yu.G. and Kamchatnov, A.M , Two-dimensional periodic waves in supersonic flow of a Bose-Einstein condensate, Journ Phys A: Math Theor 40 (2007) 611-619. pdf Gladush, Yu.G. , El, G.A., Gammal, A. and Kamchatnov, A.M., Radiation of linear waves in stationary flow of Bose-Einstein condensate past an obstacle, Phys Rev A 75 (2007) Art No 033619. pdf
2006 El, G.A., Gammal, A. and Kamchatnov, A.M, Oblique dark solitons in a supersonic flow of Bose-Einstein condensate, Phys Rev Lett, 97 (2006) Art No 180405. pdf El, G.A., Grimshaw, R.H.J. and Smyth, N.F., Unsteady undular bores in fully nonlinear shallow-water theory, Phys Fluids, 18 (2006) Art No 027104. pdf
El, G.A. and Kamchatnov, A.M.,
Spatial dispersive
shock waves generated in supersonic flow of Bose-Einstein condensate past
slender body, Phys Lett A, 350 (2006) 192-196;
pdf;
2005 El, G.A. and Kamchatnov, A.M., Kinetic equation for a dense soliton gas, Phys Rev Lett 95 (2005) Art No 204101. pdf
El, G.A.,
Resolution of a shock in
hyperbolic systems modified by weak dispersion,
CHAOS, 15 (2005)
Art No
037103, pdf,
El, G.A. , Grimshaw
R.H.J. and Kamchatnov, A.M.,
Wave
breaking and the generation of undular bores in an integrable shallow-water
system, Stud Appl Math, 114 (2005) 395-411. El, G.A., Khodorovskii, V.V., and Tyurina, A.V., Undular bore transition in bi-directional conservative wave dynamics, Physica D 206 (2005) 232-251.pdf
El, G.A., Grimshaw
R.H.J. and Kamchatnov, A.M.,
Analytic model for a weakly dissipative
shallow-water undular bore, CHAOS 15
(2005) Art
No
037102,
pdf.
2004 El, G.A., Khodorovskii, V.V., and Tyurina, A.V., Hypersonic flow past bodies in dispersive hydrodynamics, Phys Lett A, 333 (2004) 334-340.
2003
El, G.A.,
The
thermodynamic limit of the Whitham equations, Phys Lett A, 311 (2003)
374-383.
El, G.A., Khodorovskii,
V.V. and Tyurina, A.V.,
Determination of the boundaries
of expanding oscillatory zone in asymptotic solutions of non-integrable dispersive
wave equations, Phys Lett A 318
(2003) 526-537.
2002 El, G.A. and Grimshaw, R.H.J., Generation of undular bores in the shelves of slowly-varying solitary waves, CHAOS 12 (2002) 1015-1026.
2001
El, G.A., Krylov,
A.L. and Venakides, S.,
Unified approach to KdV modulations,
Commun Pure Appl Math 54 (2001)
1243-1270.
El, G.A., Grimshaw,
R.H.J., Pavlov, M.V.,
Integrable
shallow-water equations and undular bores,
Stud Appl Math 106 (2001)
157-186.
El, G.A., Krylov
A.L., Molchanov, S.A.
and Venakides, S.,
Soliton turbulence as a thermodynamic limit of stochastic soliton
lattices, Advances in Nonlinear Mathematics and Science, Physica D 152/153 (2001)
653-664.
Lukyanov, A.,
El,
G., Molokov, S.,
Instability of MHD-modified interfacial gravity waves
revisited, Phys Lett A 290 (2001) 165 -172.
1990 -- 2000
Krylov, A.L. and El, G.A.,
A stochastic
description of finite-gap potentials, RUSSIAN MATH SURVEYS, 54
(1999) 439-440 Tyurina A.V. and El, G.A., Hydrodynamics of modulated finite-amplitude waves in dispersive hydrodynamics, JOURN EXP THEOR PHYS, 88 (1999) 615-625 Gurevich, A.V., Zybin, K.P. and El, G.A., Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg-de Vries equation, JOURN EXP THEOR PHYS, 88 (1999) 182-195
Mazur, N.G., Nikolayevskii,
V.N. and El, G.A., Energy exchange between seismic and
ultrasonic vibrations in an
elastic medium with microstructure, JOURN
APPL MATHS MECH, 61 (1997)
325-328 Kamchatnov, A.M., Krylov, A.L. and El, G.A., On the asymptotic evolution of a localized perturbation for the one-dimensional Landau-Lifshits equation with uniaxial anisotropy, THEOR MATH PHYS 109 (1996) 1345-1351 El, G.A., Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem, PHYS LETT A, 222 (1996) 393-399 Gurevich A.V., Krylov A.L., Khodorovsky, V.V. and El, G.A., Supersonic flow past finite-length bodies in dispersive hydrodynamics, JOURN EXP THEOR PHYS, 82 (1996) 709-718 El, G.A., Geogjaev, V.V., Gurevich, A.V. and Krylov, A.L., Decay of an initial discontinuity in the defocusing NLS hydrodynamics, PHYSICA D, 87 (1995) 186-192 Gurevich A.V., Krylov A.L., Khodorovsky V.V. and El G.A., Supersonic flow past bodies in dispersive hydrodynamics, JOURN EXP THEOR PHYS 81 (1995) 87-96 El, G.A.. and Krylov A.V., General solution of the Cauchy problem for the defocusing NLS equation in the Whitham limit, PHYS. LETT. A, 203 (1995) 77-82
El,
G.A. and Khodorovsky, V.V., Evolution
of a solitonless large-scale perturbation in Korteweg
- de Vries hydrodynamics,
PHYS.LETT. A, 182 (1993). 49-52
El, G.A., Gurevich, A.V., Khodorovskii, V.V.and Krylov, A.L., Modulational
instability and formation of a nonlinear
oscillatory structure in a “focusing”
medium, PHYS. LETT A, 177 (1993) 357-361
Krylov,
A.L., Nikolayevskii, V.N., Mazur, NG and El, G.A., ,Gradient-consistent non-linear model of the
generation of ultrasound in the
propagation of seismic waves, J. APPL. MATHS. MECH., 57 (1993) 1057-1064
Gurevich, A.V., Krylov, A.L., El,
G.A., Quasilongitudinal nonlinear dispersive MHD waves, SOV. PHYS. JETP, 75 (1992) 825-832
Gurevich, A.V., Krylov, A.L., Mazur N.G. and
El, G.A., Evolution of a localized perturbation in Korteweg - de Vries hydrodynamics, SOVIET.
PHYS. DOKLADY, 37 (1992) 198-201
Gurevich, A.V., Krylov, A.L., and El,
G.A., Evolution
of a Riemann wave in dispersive hydrodynamics, SOV.
PHYS. JETP, 47 (1992) 957-962
Krylov, A.L., Khodorovskii, V.V., and
El, G.A., Evolution of a nonmonotonic perturbation in Korteweg - de Vries
hydrodynamics, JETP
LETT., 56 (1992)
323-327
Nikolayevskii, V.N., Krylov, A.L.
and El, G.A., Mathematical
model of
nonlinear generation of ultrasound by seismic waves, DOKL. AKAD. NAUK,
318 (1991) 1340-1345 (English translation in SOVIET PHYS DOKLADY.)
Gurevich, A.V., Krylov, A.L. and El,
G.A,
Breaking problem in dispersive hydrodynamics, JETP LETT, 54, 1991, pp.
102-107
Gurevich, A.V., Krylov, A.L. and El G.A.,
Nonlinear modulated
waves in dispersive hydrodynamics, SOV. PHYS. JETP 71
(1991) pp. 899-910
Gurevich, A.V., Krylov, A.L. and El, G.A., Nonlinear wave generation in non-isothermal plasma (modulation theory) , SOV. J. PLASMA. PHYS., 16 (1990) 139-237
Conference
Papers – Refereed 2. El, G.A., Unsteady undular bore transition in fully nonlinear conservative wave dynamics, in: Mechanics of the 21-st century, Proceedings of the 21st International Congress of Theoretical and Applied Mechanics with CD-ROM, ISBN 1-4020-3559-4 (e-book), Eds. W. Gutkowski, T.A. Kowalewski, Springer-Verlag (2005).
3. El, G.A. ,
The infinite-genus limit of the Whitham equations, Proceedings of the NEEDS - 2002 International
Conference, in: THEOR MATH PHYS, 137 (2003) 1505-1514.
4. El, G.A., Grimshaw,
R.H.J. An integrable model for undular bores on shallow water, Proceedings of the IUTAM symposium on Free
Surface Flows, A.C.King, Yu.D.Shikhmurzaev
eds, Kluwer,
5. El, G.A.,
Gurevich, A.V. and Krylov,
A.L.,
Breaking problem in dispersive hydrodynamics, in “Singular limits of dispersive waves”, N.Ercolani, I.Gabitov, D.Levermore and D.Serre
(eds.) NATO ASI series B 320, Plenum,
New York (1994) 89-104
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