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4 papers · 1 filter
The theory of optical dispersive shock waves in photorefractive media
G. A. El, A. Gammal, E. G. Khamis +2
The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whit…
Evolution of solitary waves and undular bores in shallow-water flows over a gradual slope with bottom friction
G. A. El, R. H. J. Grimshaw, A. M. Kamchatnov
This paper considers the propagation of shallow-water solitary and nonlinear periodic waves over a gradual slope with bottom friction in the framework of a variable-coefficient Kor…
Wave breaking and the generation of undular bores in an integrable shallow-water system
G. A. El, R. H. J. Grimshaw, A. M. Kamchatnov
The generation of an undular bore in the vicinity of a wave-breaking point is considered for the integrable Kaup-Boussinesq shallow water system. In the framework of the Whitham mo…
On asymptotically equivalent shallow water wave equations
H. R. Dullin, G. A. Gottwald, D. D. Holm
The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic…