54 citations · 142 across the 13 of their papers we have counts for
13 papers
Heteroclinic connections between finite-amplitude periodic orbits emerging from a codimension two singularity
Thomas J. Bridges, David J. B. Lloyd, Daniel J. Ratliff +1
Heteroclinic connections between two distinct hyperbolic periodic orbits in conservative systems are important in a wide range of applications. On the other hand, it is theoretical…
Rogue waves in extended Gross-Pitaevskii Models with a Lee-Huang-Yang correction
Sathyanarayanan Chandramouli, Simeon I. Mistakidis, Garyfallia C. Katsimiga +3
We explore the existence and dynamical generation of rogue waves (RWs) within a one dimensional quantum droplet bearing environment. RWs are computed by deploying a spacetime fixed…
Modulation leading to frequency downshifting of water waves in the vicinity of the Benjamin-Feir transition
Daniel J. Ratliff, Olga Trichtchenko, Thomas J. Bridges
For Stokes waves in finite depth within the neighbourhood of the Benjamin-Feir stability transition, there are two families of periodic waves, one modulationally unstable and the o…
The Nonlinear Evolution of Whistler-Mode Chorus Revisited: Modulation Instability as the Source of Tones
Daniel Ratliff, Oliver Allanson
We review the modulation stability of parallel propagating/field aligned Whistler Mode Chorus waves propagating in a warm plasma from a formal perspective with a focus on wave-part…
Reappraisal of Whitham's 1967 theory for wave-mean flow interaction in shallow water
Thomas J. Bridges, Daniel J. Ratliff
The modulation equations for Stokes waves in shallow water coupled to wave generated mean flow, derived in Whitham (1967), based on an averaged Lagrangian are revisited. Firstly, i…
Kink-antikink stripe interactions in the two-dimensional sine-Gordon equation
R. Carretero-Gonzalez, L. A. Cisneros-Ake, R. Decker +4
The main focus of the present work is to study quasi-one-dimensional kink-antikink stripes embedded in the two-dimensional sine-Gordon equation. Using variational techniques, we re…
Density Distribution in Soft Matter Crystals and Quasicrystals
Priya Subramanian, Daniel J. Ratliff, Alastair M. Rucklidge +1
The density distribution in solids is often represented as a sum of Gaussian peaks (or similar functions) centred on lattice sites or via a Fourier sum. Here, we argue that represe…
Genuine Nonlinearity and its Connection to the Modified Korteweg - de Vries Equation in Phase Dynamics
Daniel James Ratliff
The study of hyperbolic waves involves various notions which help characterise how these structures evolve. One important facet is the notion of \emph{genuine nonlinearity}, namely…
Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory
Thomas J. Bridges, Daniel J. Ratliff
The multiphase Whitham modulation equations with phases have characteristics which may be of hyperbolic or elliptic type. In this paper a nonlinear theory is developed for…
Spatiotemporal chaos and quasipatterns in coupled reaction-diffusion systems
Jennifer K. Castelino, Daniel J. Ratliff, Alastair M. Rucklidge +2
In coupled reaction-diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between the…
Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
Andrew J. Archer, Daniel J. Ratliff, Alastair M. Rucklidge +1
Phase field crystal (PFC) theory, extensively used for modelling the structure of solids, can be derived from dynamical density functional theory (DDFT) via a sequence of approxima…
Which wavenumbers determine the thermodynamic stability of soft matter quasicrystals?
D. J. Ratliff, A. J. Archer, P. Subramanian +1
For soft matter to form quasicrystals an important ingredient is to have two characteristic lengthscales in the interparticle interactions. To be more precise, for stable quasicrys…
Phase Dynamics of the Dysthe equation and the Bifurcation of Plane Waves
Daniel James Ratliff
The bifurcation of plane waves to localised structures is investigated in the Dysthe equation, which incorporates the effects of mean flow and wave steepening. Through the use of p…