Search Results - "Grimshaw, Rhj"

Rogue waves: analytical predictions by Grimshaw, R. H. J., Tovbis, A.

“…Rogue waves observed in the ocean and elsewhere are often modelled by certain solutions of the nonlinear Schrodinger equation, describing the modulational…”
Get full text

Two-soliton interaction as an elementary act of soliton turbulence in integrable systems by Pelinovsky, E.N., Shurgalina, E.G., Sergeeva, A.V., Talipova, T.G., El, G.A., Grimshaw, R.H.J.

“…Two-soliton interactions play a definitive role in the formation of the structure of soliton turbulence in integrable systems. To quantify the contribution of…”
Get full text

Internal rogue waves in stratified flows and the dynamics of wave packets by Liu, T.Y., Chan, H.N., Grimshaw, R.H.J., Chow, K.W.

“…A theoretical study on the occurrence of internal rogue waves in density stratified flows is conducted. While internal rogue waves for long wave models have…”
Get full text

The Reduced Ostrovsky Equation: Integrability and Breaking by Grimshaw, R. H. J., Helfrich, Karl, Johnson, E. R.

“…The reduced Ostrovsky equation is a modification of the Korteweg‐de Vries equation, in which the usual linear dispersive term with a third‐order derivative is…”
Get full text

Water Wave Packets Over Variable Depth by Grimshaw, R. H. J., Annenkov, S. Y.

“…In this paper, we develop higher‐order nonlinear Schrödinger equations with variable coefficients to describe how a water wave packet will deform and…”
Get full text

Interactions of breathers and solitons in the extended Korteweg–de Vries equation by Chow, K.W., Grimshaw, R.H.J., Ding, E.

“…The extended Korteweg–de Vries model governs the evolution of weakly dispersive waves under the combined influence of quadratic and cubic nonlinearities, and…”
Get full text

Modulational instability of two pairs of counter-propagating waves and energy exchange in a two-component system by Griffiths, S.D., Grimshaw, R.H.J., Khusnutdinova, K.R.

“…The modulational instability of two pairs of plane counter-propagating waves in a two-component system is considered within the framework of two coupled…”
Get full text

Analytic model for a weakly dissipative shallow-water undular bore by El, G A, Grimshaw, R H J, Kamchatnov, A M

“…We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile…”
Get more information

Atmospheric gravity waves in the Red Sea: a new hotspot by Magalhaes, J. M., Araújo, I. B., da Silva, J. C. B., Grimshaw, R. H. J., Davis, K., Pineda, J.

“…The region of the Middle East around the Red Sea (between 32° E and 44° E longitude and 12° N and 28° N latitude) is a currently undocumented hotspot for…”
Get full text

Transcritical Flow Over a Hole by Grimshaw, R. H. J., Zhang, D.-H., Chow, K. W.

“…Transcritical flow over a localized obstacle generates upstream and downstream nonlinear wavetrains. In the weakly nonlinear long‐wave regime, this flow has…”
Get full text

Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean by Grimshaw, Rhj, Ostrovsky, La, Shrira, Vi, Stepanyants, Yu A

“…Nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed. Attention is focussed upon…”
Get full text

Integrable Shallow-Water Equations and Undular Bores by El, G. A., Grimshaw, R. H. J., Pavlov, M. V.

“…On the basis of the integrable Kaup–Boussinesq version of the shallow‐water equations, an analytical theory of undular bores is constructed. A complete…”
Get full text

Wave Breaking and the Generation of Undular Bores in an Integrable Shallow Water System by El, G. A., Grimshaw, R. H. J., Kamchatnov, A. M.

“…The generation of an undular bore in the vicinity of a wave‐breaking point is considered for the integrable Kaup–Boussinesq (KB) shallow water system. In the…”
Get full text

Structural transformation of eigenvalues for a perturbed algebraic soliton potential by Pelinovsky, Dmitry E, Grimshaw, Roger H.J

“…We present a modified perturbation technique for the AKNS spectral system to evaluate eigenvalues supported by a perturbed algebraic soliton potential. The…”
Get full text

Internal waves in a three-layer bubbly waveguide by Grimshaw, R.H.J., Khusnutdinova, K.R.

“…In many oceanic situations, clouds, or layers of bubbles are present which may influence the larger-scale dynamics. A two-dimensional model of a diluted…”
Get full text

The effect of a depth-dependent bubble distribution on the normal modes of internal waves: quasistatic approximation by Grimshaw, R.H.J., Khusnutdinova, K.R., Ostrovsky, L.A.

“…We consider internal and surface waves propagating horizontally in the fluid waveguide, formed by an underlying density stratification. As well as the usual…”
Get full text

Solitons in nonintegrable systems by Grimshaw, Roger H J, Ostrovsky, Lev A, Pelinovsky, Dmitry E

“…We introduce the concept of this special focus issue on solitons in nonintegrable systems. A brief overview of some recent developments is provided, and the…”
Get more information

An asymptotic approach to solitary wave instability and critical collapse in long-wave KdV-type evolution equations by Pelinovsky, Dmitry E., Grimshaw, Roger H.J.

“…Instability development and critical collapse of solitary waves are considered in the framework of generalized Korteweg-de Vries (KdV) equations in one and two…”
Get full text

Terminal Damping of a Solitary Wave Due to Radiation in Rotational Systems by Grimshaw, R. H. J., He, J.-M., Ostrovsky, L. A.

“…The evolution of a solitary wave under the action of rotation is considered within the framework of the rotation‐modified Korteweg–de Vries equation. Using an…”
Get full text

The two-parameter soliton family for the interaction of a fundamental and its second harmonic by Grimshaw, R.H.J., Kuznetsov, E.A., Shapiro, E.G.

“…For a system of interacting fundamental and second harmonics, the soliton family is characterized by two independent parameters, a soliton potential and a…”
Get full text