Ablowitz, Mark J.; Cole, Justin T.; El, Gennady A.; Hoefer, Mark A.; Luo, Xu-Dan Soliton-mean field interaction in Korteweg-de Vries dispersive hydrodynamics. (English) Zbl 1528.35144 Stud. Appl. Math. 151, No. 3, 795-856 (2023). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q53 35Q35 76L05 76P05 37K15 35C08 35B20 35B40 35R09 65M70 65M06 65N35 PDFBibTeX XMLCite \textit{M. J. Ablowitz} et al., Stud. Appl. Math. 151, No. 3, 795--856 (2023; Zbl 1528.35144) Full Text: DOI arXiv
Congy, T.; El, G. A.; Roberti, G.; Tovbis, A. Dispersive hydrodynamics of soliton condensates for the Korteweg-de Vries equation. (English) Zbl 1527.35347 J. Nonlinear Sci. 33, No. 6, Paper No. 104, 45 p. (2023). MSC: 35Q53 35Q35 35C08 35R09 37K10 37K15 37K35 37K40 35L60 76L05 76P05 82C40 82D05 35R60 PDFBibTeX XMLCite \textit{T. Congy} et al., J. Nonlinear Sci. 33, No. 6, Paper No. 104, 45 p. (2023; Zbl 1527.35347) Full Text: DOI arXiv OA License
Bonnemain, Thibault; Doyon, Benjamin; El, Gennady Generalized hydrodynamics of the KdV soliton gas. (English) Zbl 1514.76058 J. Phys. A, Math. Theor. 55, No. 37, Article ID 374004, 49 p. (2022). MSC: 76M28 35Q35 81V70 35Q53 PDFBibTeX XMLCite \textit{T. Bonnemain} et al., J. Phys. A, Math. Theor. 55, No. 37, Article ID 374004, 49 p. (2022; Zbl 1514.76058) Full Text: DOI arXiv
El, Gennady A. Soliton gas in integrable dispersive hydrodynamics. (English) Zbl 07430626 J. Stat. Mech. Theory Exp. 2021, No. 11, Article ID 114001, 69 p. (2021). MSC: 82-XX PDFBibTeX XMLCite \textit{G. A. El}, J. Stat. Mech. Theory Exp. 2021, No. 11, Article ID 114001, 69 p. (2021; Zbl 07430626) Full Text: DOI arXiv
van der Sande, Kiera; El, Gennady A.; Hoefer, Mark A. Dynamic soliton-mean flow interaction with non-convex flux. (English) Zbl 1496.76035 J. Fluid Mech. 928, Paper No. A21, 43 p. (2021). MSC: 76B25 76B55 35Q51 35Q53 PDFBibTeX XMLCite \textit{K. van der Sande} et al., J. Fluid Mech. 928, Paper No. A21, 43 p. (2021; Zbl 1496.76035) Full Text: DOI arXiv
Maiden, M. D.; Franco, N. A.; Webb, E. G.; El, G. A.; Hoefer, M. A. Solitary wave fission of a large disturbance in a viscous fluid conduit. (English) Zbl 1430.76087 J. Fluid Mech. 883, Paper No. A10, 31 p. (2020). MSC: 76B25 PDFBibTeX XMLCite \textit{M. D. Maiden} et al., J. Fluid Mech. 883, Paper No. A10, 31 p. (2020; Zbl 1430.76087) Full Text: DOI arXiv
Congy, Thibault; El, G. A.; Hoefer, M. A. Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves. (English) Zbl 1419.76082 J. Fluid Mech. 875, 1145-1174 (2019). MSC: 76B15 35Q53 76B25 PDFBibTeX XMLCite \textit{T. Congy} et al., J. Fluid Mech. 875, 1145--1174 (2019; Zbl 1419.76082) Full Text: DOI arXiv
El, G. A.; Nguyen, L. T. K.; Smyth, N. F. Dispersive shock waves in systems with nonlocal dispersion of Benjamin-Ono type. (English) Zbl 1391.76079 Nonlinearity 31, No. 4, 1392-1416 (2018). MSC: 76B25 76B15 76B55 PDFBibTeX XMLCite \textit{G. A. El} et al., Nonlinearity 31, No. 4, 1392--1416 (2018; Zbl 1391.76079) Full Text: DOI arXiv
El, Gennady A.; Hoefer, Mark A.; Shearer, Michael Stationary expansion shocks for a regularized Boussinesq system. (English) Zbl 1388.35153 Stud. Appl. Math. 140, No. 1, 27-47 (2018). MSC: 35Q35 76B15 76L05 35B40 65T50 65L06 35C20 35B65 PDFBibTeX XMLCite \textit{G. A. El} et al., Stud. Appl. Math. 140, No. 1, 27--47 (2018; Zbl 1388.35153) Full Text: DOI arXiv
Hoefer, M. A.; El, G. A.; Kamchatnov, A. M. Oblique spatial dispersive shock waves in nonlinear Schrödinger flows. (English) Zbl 1376.37128 SIAM J. Appl. Math. 77, No. 4, 1352-1374 (2017). MSC: 37N10 35C08 35Q55 76L05 35L67 37K40 PDFBibTeX XMLCite \textit{M. A. Hoefer} et al., SIAM J. Appl. Math. 77, No. 4, 1352--1374 (2017; Zbl 1376.37128) Full Text: DOI arXiv
El, G. A.; Hoefer, M. A.; Shearer, M. Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws. (English) Zbl 1364.35307 SIAM Rev. 59, No. 1, 3-61 (2017). Reviewer: Piotr Biler (Wrocław) MSC: 35Q53 35L65 74J30 35C07 PDFBibTeX XMLCite \textit{G. A. El} et al., SIAM Rev. 59, No. 1, 3--61 (2017; Zbl 1364.35307) Full Text: DOI arXiv
Tovbis, Alexander; El, Gennady A. Semiclassical limit of the focusing NLS: Whitham equations and the Riemann-Hilbert problem approach. (English) Zbl 1415.35256 Physica D 333, 171-184 (2016). MSC: 35Q55 37K10 30F30 81Q20 PDFBibTeX XMLCite \textit{A. Tovbis} and \textit{G. A. El}, Physica D 333, 171--184 (2016; Zbl 1415.35256) Full Text: DOI arXiv
El, G. A.; Hoefer, M. A. Dispersive shock waves and modulation theory. (English) Zbl 1415.76001 Physica D 333, 11-65 (2016). MSC: 76-02 35-02 76L05 35Q35 35Q53 35Q55 PDFBibTeX XMLCite \textit{G. A. El} and \textit{M. A. Hoefer}, Physica D 333, 11--65 (2016; Zbl 1415.76001) Full Text: DOI arXiv Link
Biondini, G. (ed.); El, G. A. (ed.); Hoefer, M. A. (ed.); Miller, P. D. (ed.) Dispersive hydrodynamics: Preface. (English) Zbl 1415.00009 Physica D 333, 1-5 (2016). MSC: 00B15 35-06 37-06 76-06 PDFBibTeX XMLCite \textit{G. Biondini} (ed.) et al., Physica D 333, 1--5 (2016; Zbl 1415.00009) Full Text: DOI Link
El, G. A. Critical density of a soliton gas. (English) Zbl 1390.37122 Chaos 26, No. 2, 023105, 6 p. (2016). MSC: 37K40 37K10 82D05 81Q05 PDFBibTeX XMLCite \textit{G. A. El}, Chaos 26, No. 2, 023105, 6 p. (2016; Zbl 1390.37122) Full Text: DOI arXiv
Pavlov, M. V.; Taranov, V. B.; El, G. A. Generalized hydrodynamic reductions of the kinetic equation for a soliton gas. (English. Russian original) Zbl 1282.82033 Theor. Math. Phys. 171, No. 2, 675-682 (2012); translation from Teor. Mat. Fiz. 171, No. 2, 294-302 (2012). MSC: 82C70 82C40 PDFBibTeX XMLCite \textit{M. V. Pavlov} et al., Theor. Math. Phys. 171, No. 2, 675--682 (2012; Zbl 1282.82033); translation from Teor. Mat. Fiz. 171, No. 2, 294--302 (2012) Full Text: DOI arXiv Link
El, G. A.; Khodorovskii, V. V.; Leszczyszyn, A. M. Refraction of dispersive shock waves. (English) Zbl 1458.76087 Physica D 241, No. 18, 1567-1587 (2012). MSC: 76N30 76L05 35Q55 PDFBibTeX XMLCite \textit{G. A. El} et al., Physica D 241, No. 18, 1567--1587 (2012; Zbl 1458.76087) Full Text: DOI arXiv Link
El, G. A.; Kamchatnov, A. M.; Pavlov, M. V.; Zykov, S. A. Kinetic equation for a soliton gas and Its hydrodynamic reductions. (English) Zbl 1252.37056 J. Nonlinear Sci. 21, No. 2, 151-191 (2011). MSC: 37K10 37K40 35L60 PDFBibTeX XMLCite \textit{G. A. El} et al., J. Nonlinear Sci. 21, No. 2, 151--191 (2011; Zbl 1252.37056) Full Text: DOI arXiv Link
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F. Asymptotic description of solitary wave trains in fully nonlinear shallow-water theory. (English) Zbl 1155.35424 Physica D 237, No. 19, 2423-2435 (2008). MSC: 35Q51 35Q35 76B25 PDFBibTeX XMLCite \textit{G. A. El} et al., Physica D 237, No. 19, 2423--2435 (2008; Zbl 1155.35424) Full Text: DOI arXiv Link
El, G. A.; Grimshaw, R. H. J.; Smyth, N. F. Unsteady undular bores in fully nonlinear shallow-water theory. (English) Zbl 1185.76454 Phys. Fluids 18, No. 2, Art. 027104, 17p. (2006). MSC: 76B15 PDFBibTeX XMLCite \textit{G. A. El} et al., Phys. Fluids 18, No. 2, Art. 027104, 17p. (2006; Zbl 1185.76454) Full Text: DOI arXiv
El, G. A. Resolution of a shock in hyperbolic systems modified by weak dispersion. (English) Zbl 1144.37341 Chaos 15, No. 3, 037103, 21 p. (2005). MSC: 35L67 35Q53 76L05 PDFBibTeX XMLCite \textit{G. A. El}, Chaos 15, No. 3, 037103, 21 p. (2005; Zbl 1144.37341) Full Text: DOI arXiv Link
El, G. A.; Khodorovskii, V. V.; Tyurina, A. V. Undular bore transition in bi-directional conservative wave dynamics. (English) Zbl 1073.35161 Physica D 206, No. 3-4, 232-251 (2005). MSC: 35L67 PDFBibTeX XMLCite \textit{G. A. El} et al., Physica D 206, No. 3--4, 232--251 (2005; Zbl 1073.35161) Full Text: DOI
El, G. A.; Grimshaw, R. H. J. Generation of undular bores in the shelves of slowly-varying solitary waves. (English) Zbl 1080.76506 Chaos 12, No. 4, 1015-1026 (2002). MSC: 76B15 76B25 86A05 PDFBibTeX XMLCite \textit{G. A. El} and \textit{R. H. J. Grimshaw}, Chaos 12, No. 4, 1015--1026 (2002; Zbl 1080.76506) Full Text: DOI Link
El, Gennady A.; Krylov, Alexander L.; Venakides, Stephanos Unified approach to KdV modulations. (English) Zbl 1032.35156 Commun. Pure Appl. Math. 54, No. 10, 1243-1270 (2001). MSC: 35Q53 37K20 PDFBibTeX XMLCite \textit{G. A. El} et al., Commun. Pure Appl. Math. 54, No. 10, 1243--1270 (2001; Zbl 1032.35156) Full Text: DOI arXiv Link
El, G. A. Generating function of the Whitham-KdV hierarchy and effective solution of the Cauchy problem. (English) Zbl 1037.35503 Phys. Lett., A 222, No. 6, 393-399 (1996). MSC: 35Q53 37K10 PDFBibTeX XMLCite \textit{G. A. El}, Phys. Lett., A 222, No. 6, 393--399 (1996; Zbl 1037.35503) Full Text: DOI
El, G. A.; Geogjaev, V. V.; Gurevich, A. V.; Krylov, A. L. Decay of an initial discontinuity in the defocusing NLS hydrodynamics. (English) Zbl 1194.35407 Physica D 87, No. 1-4, 186-192 (1995). MSC: 35Q55 PDFBibTeX XMLCite \textit{G. A. El} et al., Physica D 87, No. 1--4, 186--192 (1995; Zbl 1194.35407) Full Text: DOI