It is well known that the existence of traveling wave solutions (TWS) for many partial differential equations (PDE) a consequence fact an associated planar ordinary equation (ODE) has certain types defined all time. In this paper we address problem persistence TWS given PDE under small perturbations. Our main results deal with situation where ODE center and, as consequence, original continuum p...

We propose a novel approach for bridging the Boussinesq equations and the primitive equations. This approach uses spatio-temporal filtering as an alternative to traditional scaling arguments. © 2009 Elsevier Ltd. All rights reserved.

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A Boussinesq-type model is derived which is accurate to O(kh) 4 and which retains the full representation of the fluid kinematics in nonlinear surface boundary condition terms, by not assuming weak nonlinearity. The model is derived for a horizontal bottom , and is based explicitly on a fourth-order polynomial representation of the vertical dependence of the velocity potential. In order to achi...

Magnetosonic waves are intensively studied due to their importance in space plasmas and also in fusion plasmas where they are used in particle acceleration and heating experiments. In the present paper we investigate the magnetosonic waves propagating in a multi-ionspecies plasma perpendicular to an external magnetic field. Due to the presence of several ion species, this mode splits into two b...

This paper discusses several algorithmic ways of constructing integrable evolution equations based on Lie algebraic structure. We derive, in a pedagogical style, a large class of two component peakon type dual systems from their two component soliton equations counter part. We study the essential aspects of Hamiltonian flows on coadjoint orbits of the centrally extended semidirect product group...

This paper presents a numerical model based on one-dimensional Beji and Nadaoka's Extended Boussinesq equations for simulation of periodic wave shoaling and its decomposition over morphological beaches. A unique Galerkin finite element and Adams-Bashforth-Moulton predictor-corrector methods are employed for spatial and temporal discretization, respectively. For direct application of linear fini...

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...

We investigate the effects mode truncation and dissipation characteristics have on predictions of wave shape statistics such as skewness and asymmetry. We demonstrate the effect of mode truncation by calculating wave shape statistics for data from a laboratory experiment using an increasing number of frequency components each calculation. We find that the values of skewness and asymmetry conver...

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each ...