208 citations · 994 across the 36 of their papers we have counts for
16 papers · 1 filter
Boussinesq-Klein-Gordon and Ostrovsky equations: evolution of cnoidal waves with local defects
Korsarun Nirunwiroj, Dmitri Tseluiko, Karima Khusnutdinova
The Boussinesq-Klein-Gordon (BKG) equation has emerged in the studies of nonlinear bulk strain waves in layered solid waveguides. The developed bi-directional weakly-nonlinear solu…
Solitary waves of moderate amplitude and dispersive radiation in the Serre equations: the extended KdV-Whitham approximation
Benjamin Martin, Dmitri Tseluiko, Karima Khusnutdinova
We consider the extended Korteweg-de Vries (eKdV) equation as a model for long moderately nonlinear surface water waves and use it to describe the evolution of initial conditions g…
Periodic solutions of coupled Boussinesq equations and Ostrovsky-type models free from zero-mass contradiction
K. R. Khusnutdinova, M. R. Tranter
Coupled Boussinesq equations describe long weakly-nonlinear longitudinal strain waves in a bi-layer with a soft bonding between the layers (e.g. a soft adhesive). From the mathemat…
Undular Bores Generated by Fracture
C. G. Hooper, P. D. Ruiz, J. M. Huntley +1
Undular bores, or dispersive shock waves, are non-stationary waves propagating as oscillatory transitions between two basic states, in which the oscillatory structure gradually exp…
Nonlinear Longitudinal Bulk Strain Waves in Layered Elastic Wavegudes
Karima R. Khusnutdinova, Matthew R. Tranter
We consider long longitudinal bulk strain waves in layered waveguides using Boussinesq-type equations. The equations are developed using lattice models, and this is viewed as an ex…
Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and cubic nonlinearities
F. E. Garbuzov, Y. M. Beltukov, K. R. Khusnutdinova
We study long nonlinear longitudinal bulk strain waves in a hyperelastic rod of circular cross section within the scope of the general weakly-nonlinear elasticity leading to a mode…
Weakly-nonlinear solution of coupled Boussinesq equations and radiating solitary waves
K. R. Khusnutdinova, M. R. Tranter
Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the m…
On Boussinesq-type models for long longitudinal waves in elastic rods
F. E. Garbuzov, K. R. Khusnutdinova, I. V. Semenova
In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in orde…
D'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation
K. R. Khusnutdinova, M. R. Tranter
In this paper we construct a weakly-nonlinear d'Alembert-type solution of the Cauchy problem for a Boussinesq-Klein-Gordon equation. Similarly to our earlier work based on the use…
Radiating solitary waves in coupled Boussinesq equations
R. H. J. Grimshaw, K. R. Khusnutdinova, K. R. Moore
In this paper we are consider radiating solitary wave solutions of coupled regularised Boussinesq equations. This type of solution consists of a leading solitary wave with a small-…
On radiating solitary waves in bi-layers with delamination and coupled Ostrovsky equations
K. R. Khusnutdinova, M. R. Tranter
We study the scattering of a long longitudinal radiating bulk strain solitary wave in the delaminated area of a two-layered elastic structure with soft (`imperfect') bonding betwee…
Nonlinear ring waves in a two-layer fluid
K. R. Khusnutdinova, X. Zhang
Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation.…
Modelling of nonlinear wave scattering in a delaminated elastic bar
K. R. Khusnutdinova, M. R. Tranter
Integrity of layered structures, extensively used in modern industry, strongly depends on the quality of their interfaces; poor adhesion or delamination can lead to a failure of th…
On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation
K. R. Khusnutdinova, C. Klein, V. B. Matveev +1
There exist two versions of the Kadomtsev-Petviashvili equation, related to the Cartesian and cylindrical geometries of the waves. In this paper we derive and study a new version,…
Initial-value problem for coupled Boussinesq equations and a hierarchy of Ostrovsky equations
K. R. Khusnutdinova, K. R. Moore
We consider the initial-value problem for a system of coupled Boussinesq equations on the infinite line for localised or sufficiently rapidly decaying initial data, generating suff…
Modulational instability of two pairs of counter-propagating waves and energy exchange in two-component media
S. D. Griffiths, R. H. J. Grimshaw, K. R. Khusnutdinova
The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We co…