Journal Articles
El, G, Nguyen, K, Smyth, NF (2018)
Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type,
Nonlinearity, ISSN: 0951-7715. DOI:
10.1088/1361-6544/aaa10a.
Maiden, MD, Anderson, DV, Franco, NA,
El, G, Hoefer, MA (2018)
Solitonic dispersive hydrodynamics: theory and observation,
Physical Review Letters, ISSN: 0031-9007. DOI:
10.1103/PhysRevLett.120.144101.
Sprenger, P, Hoefer, MA,
El, G (2018)
Hydrodynamic optical soliton tunneling,
Physical Review E, ISSN: 1539-3755. DOI:
10.1103/PhysRevE.97.032218.
El, G, Hoefer, MA, Shearer, M (2017)
Stationary expansion shocks for a regularized Boussinesq system,
Studies in Applied Mathematics, ISSN: 0022-2526. DOI:
10.1111/sapm.12191.
Tikan, A, Billet, C,
El, G, Tovbis, A, Bertola, M, Sylvestre, T, Gustave, F, Randoux, S, Genty, G, Suret, P, Dudley, JM (2017)
Universality of the Peregrine soliton in the focusing dynamics of the cubic nonlinear Schrödinger equation,
Physical Review Letters, 119(3), 033901, ISSN: 0031-9007. DOI:
10.1103/PhysRevLett.119.033901.
Chesnokov, AA,
El, G, Gavrilyuk, SL, Pavlov, MV (2017)
Stability of shear shallow water flows with free surface,
SIAM Journal on Applied Mathematics, ISSN: 1095-712X. DOI:
10.1137/16M1098164.
Hoefer, MA,
El, G, Kamchatnov, AM (2017)
Oblique spatial dispersive shock waves in nonlinear Schrodinger flows,
SIAM Journal on Applied Mathematics, ISSN: 0036-1399. DOI:
10.1137/16M108882X.
Randoux, S, Gustave, F, Suret, P,
El, G (2017)
Optical random Riemann waves in integrable turbulence,
Physical Review Letters, ISSN: 1079-7114. DOI:
10.1103/PhysRevLett.118.233901.
El, GA and Hoefer, MA (2016)
Dispersive shock waves and modulation theory,
Physica D: Nonlinear Phenomena, 333, pp.11-65, ISSN: 1872-8022. DOI:
10.1016/j.physd.2016.04.006.
Bertola, M,
El, G, Tovbis, A (2016)
Rogue waves in multiphase solutions of the focusing nonlinear Schrödinger equation,
Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences, ISSN: 1364-5021. DOI:
10.1098/rspa.2016.0340.
Onorato, M, Proment, D,
El, G, Randoux, S, Suret, P (2016)
On the origin of heavy-tail statistics in equations of the Nonlinear Schrodinger type,
Physics Letters Section A: General, Atomic and Solid State Physics, ISSN: 1873-2429. DOI:
10.1016/j.physleta.2016.07.048.
Biondini, G,
El, G, Hoefer, MA, Miller, PD (2016)
Dispersive hydrodynamics: Preface,
Physica D: Nonlinear Phenomena, 333, pp.1-5, ISSN: 1872-8022. DOI:
10.1016/j.physd.2016.07.002.
El, GA, Hoefer, MA, Shearer, M (2016)
Expansion shock waves in regularised shallow water theory,
Proceedings of the Royal Society of London: Mathematical, Physical and Engineering Sciences, 472, 20160141, ISSN: 0962-8444. DOI:
10.1098/rspa.2016.0141.
Tovbis, A and
El, G (2016)
Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert Problem approach,
Physica D: Nonlinear Phenomena, 333, pp.171-184, ISSN: 0167-2789. DOI:
10.1016/j.physd.2016.03.009.
El, GA and Smyth, NF (2016)
Radiating dispersive shock waves in non-local optical media,
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 472(2187), ISSN: 1364-5021. DOI:
10.1098/rspa.2015.0633.
El, G (2016)
Critical density of a soliton gas,
Chaos, 26, ISSN: 1089-7682. DOI:
10.1063/1.4941372.
Carbone, F, Dutykh, D,
El, G (2016)
Macroscopic dynamics of incoherent soliton ensembles: soliton-gas kinetics and direct numerical modelling,
Europhysics Letters: a letters journal exploring the frontiers of physics, 113, ISSN: 1286-4854. DOI:
10.1209/0295-5075/113/30003.
El, G, Hoefer, MA, Shearer, M (2016)
Dispersive and diffusive-dispersive shock waves for non-convex conservation laws,
SIAM Review, ISSN: 0036-1445. DOI:
10.1137/15M1015650.
Randoux, S, Suret, P,
El, G (2016)
Inverse scattering transform analysis of rogue waves using local periodization procedure,
Scientific Reports, ISSN: 2045-2322. DOI:
10.1038/srep29238.
El, G, Khamis, EG, Tovbis, A (2016)
Dam break problem for the focusing nonlinear Schrodinger equation and the generation of rogue waves,
Nonlinearity, ISSN: 1361-6544. DOI:
10.1088/0951-7715/29/9/2798.
Lowman, NK, Hoefer, MA,
El, G (2014)
Interactions of large amplitude solitary waves in viscous fluid conduits,
JOURNAL OF FLUID MECHANICS, 750, pp.372-384, ISSN: 0022-1120. DOI:
10.1017/jfm.2014.273.
Kamchatnov, AM, Kuo, Y-H, Lin, T-C, Horng, T-L, Gou, S-C, Clift, R,
El, GA, Grimshaw, RHJ (2013)
Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation,
JOURNAL OF FLUID MECHANICS, 736, pp.495-531, ISSN: 0022-1120. DOI:
10.1017/jfm.2013.556.
Pelinovsky, EN, Shurgalina, EG, Sergeeva, AV, Talipova, TG,
El, GA, Grimshaw, RHJ (2013)
Two-soliton interaction as an elementary act of soliton turbulence in integrable systems,
Physics Letters, Section A: General, Atomic and Solid State Physics, 377(3-4), pp.272-275, ISSN: 0375-9601. DOI:
10.1016/j.physleta.2012.11.037.
El, GA, Grimshaw, RHJ, Tiong, WK (2012)
Transformation of a shoaling undular bore,
JOURNAL OF FLUID MECHANICS, 709, pp.371-395, ISSN: 0022-1120. DOI:
10.1017/jfm.2012.338.
Kamchatnov, AM, Kuo, YH, Lin, TC, Horng, TL, Gou, SC, Clift, R,
El, GA, Grimshaw, RHJ (2012)
Undular bore theory for the Gardner equation,
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 86(3), ISSN: 1539-3755. DOI:
10.1103/PhysRevE.86.036605.
El, GA, Khodorovskii, VV, Leszczyszyn, AM (2012)
Refraction of dispersive shock waves,
Physica D: Nonlinear Phenomena, 241(18), pp.1567-1587, ISSN: 0167-2789. DOI:
10.1016/j.physd.2012.06.002.
Pavlov, MV, Taranov, VB,
El, GA (2012)
Generalized hydrodynamic reductions of the kinetic equation for a soliton gas,
Theoretical and Mathematical Physics, 171(2), pp.675-682, ISSN: 0040-5779. DOI:
10.1007/s11232-012-0064-z.
El, GA, Khodorovskii, VV, Leszczyszyn, AM (2012) Refraction of dispersive shock waves,
Physica D: Nonlinear Phenomena, ISSN: 0167-2789.
Pelinovsky, EN, Shurgalina, EG, Sergeeva, AV, Talipova, TG,
El, GA, Grimshaw, RHJ (2012) Two-soliton interaction as an elementary act of soliton turbulence in integrable systems,
Physics Letters, Section A: General, Atomic and Solid State Physics, ISSN: 0375-9601.
Molokov, S,
El, G, Lukyanov, A (2011)
Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field,
Theoretical and Computational Fluid Dynamics, 25(5), pp.261-279, ISSN: 0935-4964. DOI:
10.1007/s00162-010-0201-y.
El, G, Kamchatnov, AM, Pavlov, MV, Zykov, SA (2011)
Kinetic equation for a soliton gas and its hydrodynamic reductions,
J Nonlin Sci, 21, pp.151-191, DOI:
10.1007/s00332-010-9080-z.
Molokov, S,
El, G, Lukyanov, A (2010) Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field,
THEOR COMP FLUID DYN (accepted), pp.1-16.
Horng, TL, Gou, SC, Lin, TC,
El, GA, Itin, AP, Kamchatnov, AM (2009) Stationary wave patterns generated by an impurity moving with supersonic velocity through a Bose-Einstein condensate,
PHYS REV A, Art No. 053619, 79, pp.1-6.
El, G, Grimshaw, RHJ, Smyth, NF (2009) Transcritical shallow-water flow past topography:finite-amplitude theory,
J. Fluid Mech.,, 640, pp.187-214.
Leszczyszyn, AM,
El, G, Yu, G, Kamchatnov, AM (2009)
Transcritical flow a Bose-Einstein condensate through a penetrable barrier,
PHYS REV A, Art No. 063608, 79, pp.1-16.
El, G, Kamchatnov, AM, Khodorovskii, VV, Annibale, ES, Gammal, A (2009)
Two-dimensional supersonic nonlinear Schrodinger flow past an extended obstacle,
PHYS REV E, Art No 046317, 80, pp.1-25.
El, G, Grimshaw, RHJ, Smyth, NF (2008) Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory,
Physica D, 237, pp.2423-2435.
Khamis, EG, Gammal, A,
El, G, Gladush, YG, Kamchatnov, AM (2008) Nonlinear diffraction of light beams propagating on photorefractive media with embedded reflecting wire,
PHYS REV A, Art No. 013829, 78, pp.1-18.
El, GA, Gammal, A, Kamchatnov, AM (2007)
Generation of oblique dark solitons in supersonic flow of Bose-Einstein condensate past an obstacle,
Nuclear Physics A, 790(1-4), pp.771c-775c, ISSN: 0375-9474. DOI:
10.1016/j.nuclphysa.2007.03.024.
El, G, Grimshaw, RHJ, Kamchatnov, AM (2007)
Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction,
J Fluid Mech, 585, pp.213-244, DOI:
10.1017/S0022112007006817.
El, G, Gladush, YG, Kamchatnov, AM (2007) Two-dimensional periodic waves in supersonic flow of a Bose-Einstein Condensate,
Journ. Phys A: Math. Theor, 40, pp.611-619.
Gladush, YG,
El, G, Gammal, A, Kamchatnov, AM (2007) Radiation of linear waves in stationary flow of Bose-Einstein condensate past an obstacle,
Phys Rev A, 75, pp.033619 (1-5).
El, G, Gammal, A, Khamis, EG, Kraenkel, RA, Kamchatnov, AM (2007)
Theory of optical dispersive shock waves in photo-refractive media,
PHYS REV A, 75, pp.Art No 033619 (1-18).
El, G, Gammal, A, Kamchatnov, AM (2006)
Oblique dark solitons in supersonic flow of a Bose-Einstein condensate,
Physical Review Letters, 97, pp.180405 (1-4), ISSN: 1079-7114. DOI:
10.1103/PhysRevLett.97.180405.
El, GA and Kamchatnov, AM (2006)
Erratum: Spatial dispersive shock waves generated in supersonic flow of Bose-Einstein condensate past slender body (Physics Letters A (2006) 350 (192),
Physics Letters, Section A: General, Atomic and Solid State Physics, 352(6), pp.554-555, ISSN: 0375-9601. DOI:
10.1016/j.physleta.2006.01.076.
El, GA and Kamchatnov, AM (2006)
Spatial dispersive shock waves generated in supersonic flow of Bose-Einstein condensate past slender body (vol 350, pg 192, 2006),
PHYSICS LETTERS A, 352(6), pp.554-555, ISSN: 0375-9601. DOI:
10.1016/j.physleta.2006.01.076.
El, GA, Grimshaw, RHJ, Smyth, NF (2006)
Unsteady undular bores in fully nonlinear shallow-water theory,
Physics Of Fluids, 18(2), pp.027104 (1-17), ISSN: 1070-6631. DOI:
10.1063/1.2175152.
El, GA and Kamchatnov, AM (2006)
Spatial dispersive shock waves generated in supersonic flow of Bose-Einstein condensate past slender body,
PHYS LETT A, 350, pp.192-196.
El, GA (2006)
Erratum: Resolution of a shock in hyperbolic systems modified by weak dispersion (Chaos (2005) 15 (037103),
Chaos, 16(2), ISSN: 1054-1500. DOI:
10.1063/1.2186766.
El, GA and Kamchatnov, AM (2005)
Kinetic equation for a dense soliton gas,
Physical Review Letters, 95, pp.204101(1-4), ISSN: 1079-7114. DOI:
10.1103/PhysRevLett.95.204101.
El, GA, Grimshaw, RHJ, Kamchatnov, AM (2005)
Analytic model for a weakly dissipative shallow-water undular bore,
CHAOS, 15(3), ARTN 037102, ISSN: 1054-1500. DOI:
10.1063/1.1914743.
El, GA (2005)
Resolution of a shock in hyperbolic systems modified by weak dispersion,
CHAOS: An Interdisciplinary Journal of Nonlinear Science, 15, pp.037103 (1-21), ISSN: 1054-1500. DOI:
10.1063/1.1947120.
El, GA, Grimshaw, RHJ, Kamchatnov, AM (2005) Analytic Model for a Weekly Dissipative Shallow-Water Undular Bore,
CHAOS 15, 3, 037102 13.
El, GA, Grimshaw, RHJ, Kamchatnov, AM (2005)
Wave Breaking and the Generation of Undular Bores in an Integral Shallow-Water System,
STUD APPL MATH, 114, pp.395-411.
El, GA, Khodorovskii, VV, Tyurina, AV (2005) Undular bore transition in bi-directional conservative wave dynamics,
Physica D, 206, pp.232-251.
El, GA, Tyurina, AV, Khodorovskii, VV (2004) Hypersonic Flow Past Slender Bodies in Dispersive Hydrodynamics,
PHYS LETT A, 333, pp.334-340.
El, GA, Tyurina, AV, Khodorovskii, VV (2003) Determination of the Boundaries of Expanding Oscillatory Zone in Asymptotic Solutions of Non-Integrable Dispersive Wave Equations,
PHYS LETT A, 311, pp.526-536.
El, GA (2003) The Thermodynamic Limit of the Whitham Equations,
PHYS LETT A, 311, pp.372-383.
El, G (2003)
The thermodynamic limit of the Whitham equations,
Physics Letters, Section A: General, Atomic and Solid State Physics, 311(4-5), pp.374-383, ISSN: 0375-9601. DOI:
10.1016/S0375-9601(03)00515-2.
El, GA and Grimshaw, RHJ (2002)
Generation of undular bores in the shelves of slowly-varying solitary waves,
CHAOS, 12, pp.1015-1026.
Ei, GA and Grimshaw, RHJ (2001)
An integrable model for undular bores on shallow water,
Fluid Mechanics and its Applications, 62, pp.99-106, ISSN: 0926-5112. DOI:
10.1007/978-94-010-0796-2_12.
El, GA, Krylov, AL, Venakides, S (2001)
Unified Approach to KdV Modulations,
Communications on Pure and Applied Mathematics, 54(10), pp.1243-1270, ISSN: 1097-0312. DOI:
10.1002/cpa.10002.
El, GA, Grimshaw, RHJ, Pavlov, MV (2001) Integrable Shallow Water Equations and Undular Bores,
Studies in Applied Mathematics, 106, pp.157-186.
El, GA, Grimshaw, RHJ, Pavlov, MV (2001) Integrable shallow-water equations and undular bores,
STUDS APPL MATH, 106, pp.157-186.
El, GA, Krylov, AL, Molchanov, SA, Venakides, S (2001) Soliton Turbulence as a Thermodynamic Limit of Stochastic Soliton Lattices,
Advances in Nonlinear Mathematics and Science. Physica D, 152/153, pp.653-664.
El, GA, Lukyanov, A, Molokov, S (2001) Instability of MHD-Modified Interfacial Gravity Waves Revisited,
PHYS LETT A, 290, pp.165-172.
Gurevich, AV, Zybin, KP,
El, G (1999) Development of stochastic oscillations in a one-dimensional dynamical system described by the Korteweg - de Vries equation,
JOURN EXP THEOR PHYS, 88, pp.182-195.
Tyurina, AV and
El, G (1999) Hydrodynamics of modulated finite-amplitude waves in dispersive hydrodynamics,
JOURN EXP THEOR PHYS, 88, pp.615-625.
Krylov, AL and
El, G (1999) A stochastic description of finite-gap potentials,
RUSSIAN MATH SURVEYS, 54, pp.439-440.
Mazur, NG, Nikolayevskii, VV,
El, G (1997) Energy exchange between seismic and ultrasonic vibrations in an elastic medium with microstructure,
JOURN APPL MATHS MECH, 61, pp.325-328.
Gurevich, AV, Krylov, AL, Khodorovskii, VV,
El, GA (1996)
Supersonic flow of solid states in the dispersion hydrodynamics (ultimately extended solid states),
ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 109(4), pp.1316-1334, ISSN: 0044-4510.
Gurevich, AV, Krylov, AL, Khodorovsky, VV,
El, G (1996) Supersonic flow past finite-length bodies in dispersive hydrodynamics,
JOURN EXP THEOR PHYS, 82, pp.709-718.
El, G (1996) Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem,
PHYS LETT A, 222, pp.393-399.
Kamchatnov, AM, Krylov, AL,
El, G (1996) On the asymptotic evolution of a localized perturbation for the one-dimensional Landau-Lifshits equation with uniaxial anisotropy,
THEOR MATH PHYS, 109, pp.1345-1351.
GUREVICH, AV, KRYLOV, AL, KHODOROVSKII, VV,
EL, GA (1995)
SUPERSONIC-FLOW OF SOLID STATES IN DISPERSION HYDRODYNAMICS,
ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 108(1), pp.163-181, ISSN: 0044-4510.
El, G and Krylov, AV (1995) General solution solution of the Cauchy problem for the defocusing NLS equation in the Whitham limit,
PHYS. LETT. A, 203, pp.77-82.
Gurevich, AV, Krylov, AL, Khodorovsky, VV,
El, G (1995) Supersonic flow past bodies in dispersive hydrodynamics,
JOURN EXP THEOR PHYS, 80, pp.87-96.
El, G, Geogjaev, VV, Gurevich, AV, Krylov, AL (1995) Decay of an initial discontinuity in the defocusing NLS hydrodynamics,
PHYSICA D, 87, pp.186-192.
Krylov, AL, Mazur, NG, Nikolaevskij, VN, El', GA (1993) A grade-consistent nonlinear model for ultrasound generation in seismic wave propagation,
Prikladnaya Matematika i Mekhanika, 57(6), pp.100-109, ISSN: 0032-8235.
Krylov, AL, Nikolayevskii, VN, Mazur, NG,
El, G (1993) Gradient-consistent non-linear model of the generation of ultrasound in the propagation of seismic waves,
J. APPL. MATHS. MECH, 57, pp.1057-1064.
El, G, Gurevich, AV, Khodorovskii, VV, Krylov, AL (1993) Modulational instability and formation of a nonlinear oscillatory structure in a "focusing medium",
PHYS. LETT. A, 177, pp.357-361.
El, G and Khodorovsky, VV (1993) Evolution of a solitonless large-scale perturbation in Korteweg - de Vries hydrodynamics,
PHYS. LETT. A, 182, pp.49-52.
GUREVICH, AV, KRYLOV, AL,
EL, GA (1992)
QUASIPARALLEL NONLINEAR DISPERSIVE MHD-WAVES,
ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 102(5), pp.1524-1539, ISSN: 0044-4510.
GUREVICH, AV, KRYLOV, AL,
EL, GA (1992)
EVOLUTION OF A RIEMANN WAVE IN THE DISPERSIVE HYDRODYNAMICS,
ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 101(6), pp.1797-1807, ISSN: 0044-4510.
Gurevich, AV, Krylov, AL, Mazur, NG,
El, G (1992) Evolution of a localized perturbation in Korteweg - de Vries hydrodynamics,
SOVIET. PHYS. DOKLADY, 37, pp.198-201.
Gurevich, AV, Krylov, AL,
El, G (1992) Quasilongitudinal nonlinear dispersive MHD waves,
SOV. PHYS. JETP, 75, pp.825-832.
Krylov, AL, Khodorovskii, VV,
El, G (1992) Evolution of a nonmonotonic perturbation in Korteweg - de Vries hydrodynamics,
JETP LETT, 56, pp.323-327.
Gurevich, AV, Krylov, AL,
El, G (1992) Evolution of a Riemann wave in dispersive hydrodynamics,
SOV. PHYS. JETP, 47, pp.957-962.
GUREVICH, AV, KRYLOV, AL, MAZUR, NG,
EL, GA (1992)
EVOLUTION OF A LOCALIZED PERTURBATION IN KORTEWEG-DEVRIES HYDRODYNAMICS,
DOKLADY AKADEMII NAUK, 323(5), pp.876-879, ISSN: 0869-5652.
GUREVICH, AV, KRYLOV, AL,
EL, GA (1991)
BREAKING OF A RIEMANN WAVE IN DISPERSIVE HYDRODYNAMICS,
JETP LETTERS, 54(2), pp.102-107, ISSN: 0021-3640.
Gurevich, AV, Krylov, AL,
El, G (1991) Nonlinear modulated waves in dispersive hydrodynamics,
SOV. PHYS. JETP, 71, pp.899-910.
Gurevich, AV, Krylov, AL,
El, G (1991) Breaking problem in dispersive hydrodynamics,
JETP LETT, 54, pp.102-107.
Nikolayevskii, VN, Krylov, AL,
El, G (1991) Mathematical model of nonlinear generation of ultrasound by seismic waves,
DOKL. AKAD. NAUK, 318, pp.1340-1345.
GUREVICH, AV, KRYLOV, AL,
EL, GA (1990)
NONLINEAR MODULATED WAVES IN DISPERSIVE HYDRODYNAMICS,
ZHURNAL EKSPERIMENTALNOI I TEORETICHESKOI FIZIKI, 98(5), pp.1605-1626, ISSN: 0044-4510.
Gurevich, AV, Krylov, AL,
El, G (1990) Nonlinear wave generation in non-isothermal plasma (modulation theory),
SOV. J. PLASMA. PHYS, 16, pp.139-237.
Congy, T, El, GA, Hoefer, MA, Shearer, M (Accepted for publication) Nonlinear Schrödinger equations and the universal description of
dispersive shock wave structure, DOI: 10.1111/sapm.12247.
