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 …

In this article, the generalized (N+ 1)-dimensional nonlinear Boussinesq equation is
analyzed via Lie symmetry method. Lie point symmetries of the considered equation and …

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 …

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 …

The main observation of this paper is that the modified Korteweg–de Vries equation has its
natural origin in phase modulation of a basic state such as a periodic travelling wave, or …

The phase dynamics of two phase wavetrains in the coupled non-linear Schrödinger (NLS)
equations are investigated as an example of the dispersion arising from singular wave …

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 …

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 …

This paper illustrates how the singularity of the wave action flux causes the Kadomtsev‐
Petviashvili (KP) equation to arise naturally from the modulation of a two‐phased wavetrain …

Criticality plays a central role in the study of reductions and stability of hydrodynamical
systems. At critical points, it is often the case that nonlinear reductions with dispersion arise …