Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations
Phase field crystal (PFC) theory is extensively used for modeling the phase behavior,
structure, thermodynamics, and other related properties of solids. PFC theory can be derived …
structure, thermodynamics, and other related properties of solids. PFC theory can be derived …
Reappraisal of Whitham's 1967 theory for wave–meanflow interaction in shallow water
The modulation equations for Stokes waves in shallow water coupled to wave-generated
meanflow, derived in Whitham (1967), based on an averaged Lagrangian are re-visited …
meanflow, derived in Whitham (1967), based on an averaged Lagrangian are re-visited …
A proof of validity for multiphase Whitham modulation theory
TJ Bridges, A Kostianko… - Proceedings of the …, 2020 - royalsocietypublishing.org
It is proved that approximations which are obtained as solutions of the multiphase Whitham
modulation equations stay close to solutions of the original equation on a natural time scale …
modulation equations stay close to solutions of the original equation on a natural time scale …
Krein signature and Whitham modulation theory: the sign of characteristics and the “sign characteristic”
In classical Whitham modulation theory, the transition of the dispersionless Whitham
equations from hyperbolic to elliptic is associated with a pair of nonzero purely imaginary …
equations from hyperbolic to elliptic is associated with a pair of nonzero purely imaginary …
Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory
The multiphase Whitham modulation equations with N phases have 2 N characteristics
which may be of hyperbolic or elliptic type. In this paper, a nonlinear theory is developed for …
which may be of hyperbolic or elliptic type. In this paper, a nonlinear theory is developed for …
[KSIĄŻKA][B] Conservation laws, modulation and the emergence of universal forms
DJ Ratliff - 2014 - search.proquest.com
Phase modulation has been a tool used for many years to describe system behaviour about
periodic wavetrain solutions. The method has been shown to lead to well known partial …
periodic wavetrain solutions. The method has been shown to lead to well known partial …
The modulation of multiple phases leading to the modified Korteweg–de Vries equation
DJ Ratliff - Chaos: An Interdisciplinary Journal of Nonlinear …, 2018 - pubs.aip.org
This paper seeks to derive the modified Korteweg–de Vries (mKdV) equation using a novel
approach from systems generated from abstract Lagrangians possessing a two-parameter …
approach from systems generated from abstract Lagrangians possessing a two-parameter …