Dispersive shock wave theory for the Gardner equation by Richard Clift

“…Dispersive shock wave theory for the Gardner equation…”
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Undular bore theory for the Gardner equation by A.M. Kamchatnov, Y.-H. Kuo, Tai-Chia Lin, T.-L. Horng, S.-C. Gou, Richard Clift, Gennady El, Roger Grimshaw

“…We develop modulation theory for undular bores (dispersive shock waves) in the framework of the Gardner, or extended Korteweg–de Vries (KdV), equation, which is a generic mathematical model for weakly nonlinear and weakly dispersive wave propagation, when effects of higher order nonlinearity become important. …”
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Transcritical flow of a stratified fluid over topography: analysis of the forced Gardner equation by A.M. Kamchatnov, Y.-H. Kuo, Tai-Chia Lin, T.-L. Horng, S.-C. Gou, Richard Clift, Gennady El, Roger Grimshaw

“…Along with the regular, cnoidal undular bores occurring in the analogous problem for the single-layer flow modeled by the forced KdV equation, the transcritical internal wave flows support a diverse family of upstream and downstream wave structures, including kinks, rarefaction waves, classical undular bores, reversed and trigonometric undular bores, which we describe using the recent development of the nonlinear modulation theory for the (unforced) Gardner equation. …”
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How to reduce sitting time? A review of behaviour change strategies used in sedentary behaviour reduction interventions among adults by Benjamin Gardner, Lee Smith, Fabiana Lorencatto, Mark Hamer, Stuart J.H. Biddle

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Experimental and theoretical study of longitudinal undular bores generated by fracture by Curtis Hooper

“…Undular bores, or dispersive shock waves, are non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually expands and grows in amplitude with distance travelled. …”
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Weekday and weekend patterns of objectively measured sitting, standing, and stepping in a sample of office-based workers: the active buildings study by Lee Smith, Mark Hamer, Marcella Ucci, Alexi Marmot, Benjamin Gardner, Alexia Sawyer, Jane Wardle, Abigail Fisher

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Aligning material extrusion direction with mechanical stress via 5-axis tool paths by James Gardner, Tom Nethercott-Garabet, N. Kaill, Ian Campbell, Guy A. Bingham, Daniel Engstrom, N.O. Balc

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Depressive symptoms, handgrip strength, and weight status in US older adults by Lee Smith, Stephanie White, Brendon Stubbs, Liang Hu, Nicola Veronese, Davy Vancampfort, Mark Hamer, Benjamin Gardner, Lin Yang

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Damping of large-amplitude solitary waves by Roger Grimshaw, Efim N. Pelinovsky, Tatiana G. Talipova

“…However, for many cases in nonlinear wave dynamics, such as for internal solitary waves in the ocean and atmosphere, the nonlinearity is not so weak as is implied by the Korteweg-de Vries equation. …”
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Theoretical estimates of the parameters of longitudinal undular bores in polymethylmethacrylate bars based on their measured initial speeds by Curtis Hooper, Karima Khusnutdinova, Jonathan Huntley, Pablo Ruiz

“…From the wave speed and strain rate close to the fracture site, we estimate the strain rate of the release wave as well as the growth of the amplitude and duration of the leading oscillation away from the fracture site on using formulae derived from the simple analytical solution of the linearised Gardner equation (linearised near the pre-strain level at fracture). …”
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Fission of a weakly nonlinear interfacial solitary wave at a step by Roger Grimshaw, Efim N. Pelinovsky, Tatiana G. Talipova

“…The effects of cubic nonlinearity are studied in the framework of the extended Korteweg-de Vries (Gardner) equation which is also integrable. The higher-order nonlinear effects influence the amplitudes of the generated solitons if the amplitude of the transformed wave is comparable with the thickness of lower layer, but otherwise the process of soliton fission is qualitatively the same as in the framework of the Korteweg-de Vries equation.…”
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