Planar antiferroelectric liquid crystal (AFLC) cells exhibit propagating solitary waves. By measuring the retardation and the apparent tilt angle, we find that the conventional model for the solitary wave propagation in AFLCs is not generally applicable. The model being proposed here shows that the solitary wave propagation both along and normal to the smectic layer plane can be explained by a ...

The linear stability of solitary-wave or front solutions of Hamiltonian evolutionary equations, which are equivariant with respect to a Lie group, is studied. The organizing centre for the analysis is a multisymplectic formulation of Hamiltonian partial differential equations (PDEs) where a distinct symplectic operator is assigned for time and space. This separation of symplectic structures lea...

Weakly nonlinear waves in elastic rods have been studied by many authors. Most studies concentrated on smooth solutions only. However, when waves are of moderate length, non-smooth waves, such as peakons (or solitary shock waves), can arise (see Dai and Huo 2000). For strongly nonlinear waves (not assuming the smallness of the wave amplitude), as far as the authors are aware, only incompressibl...

In their proof of the stability of standing-wave solutions of nonlinear Schrödinger equations, Cazenave and Lions used the principle of concentration compactness to characterize the standing waves as solutions of a certain variational problem. In this article we first review the techniques introduced by Cazenave and Lions, and then discuss their application to solitary-wave solutions of nonloca...

This paper presents an existence theory for small-amplitude solitary-wave solutions to the classical water-wave problem in the absence of surface tension and with an arbitrary distribution of vorticity. The hydrodynamic problem is formulated as an infinite-dimensional Hamiltonian system in which the horizontal spatial direction is the time-like variable. A centre-manifold reduction technique is...

This paper re-examines existing wave run-up data for regular, irregular and solitary waves on smooth, impermeable plane slopes. A simple physical argument is used to derive a new wave run-up equation in terms of a dimensionless wave parameter representing the maximum, depth-integrated momentum flux in a wave as it reaches the toe of the structure slope. This parameter is a physically relevant d...

In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support. This is the second in a series of two p...

This paper presents a numerical model for the simulation of solitary wave transformation around a permeable submerged breakwater. The wave-structure interaction is obtained by solving the Volume-Averaged Reynolds-Averaged Navier-Stokes governing equations VARANS and volume of fluid VOF theory. This model is applied to understand the effects of porosity, equivalent mean diameter of porous media,...

Nonlinear Schrödinger equations (NLSs) with focusing power nonlinearities have solitary wave solutions. The spectra of the linearized operators around these solitary waves are intimately connected to stability properties of the solitary waves and to the long-time dynamics of solutions of NLSs. We study these spectra in detail, both analytically and numerically.