Related papers: Notes on numerical analysis and solitary wave solu…
We consider linear instability of solitary waves of several classes of dispersive long wave models. They include generalizations of KDV, BBM, regularized Boussinesq equations, with general dispersive operators and nonlinear terms. We obtain…
A higher-order nonlinear Boussinesq system with a time-dependent boundary delay is considered. Sufficient conditions are presented to ensure the well-posedness of the problem by utilizing Kato's variable norm technique and the Fixed-Point…
We perform a complete Fourier analysis of the semi-discrete 1-d wave equation obtained through a P1 discontinuous Galerkin (DG) approximation of the continuous wave equation on an uniform grid. The resulting system exhibits the interaction…
In this paper we address the Cauchy problem for two systems modeling the propagation of long gravity waves in a layer of homogeneous, incompressible and inviscid fluid delimited above by a free surface, and below by a non-necessarily flat…
We study the Boussinesq equation from the point of view of a multiple-time reductive perturbation method. As a consequence of the elimination of the secular producing terms through the use of the Korteweg--de Vries hierarchy, we show that…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
A high-frequency recovered fully discrete low-regularity integrator is constructed to approximate rough and possibly discontinuous solutions of the semilinear wave equation. The proposed method, with high-frequency recovery techniques, can…
We study a system of forced viscous shallow water equations with nontrivial bathymetry in two spatial dimensions. We develop a well-posedness theory for small but arbitrary forcing data, as well as for a fixed data profile but large…
In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et. al. [Stud. Appl. Math., 53 (1974) 249--315] and one by Hirota and…
We present a coherent and effective theoretical framework to systematically construct numerically exact nonlinear solitary waves from their respective linear limits. First, all possible linear degenerate sets are classified for a harmonic…
This article is devoted to exact solutions of the Boussinesq equation that models nonlinear shallow water waves. For this we use the Hirota bilinear method and differential constrains. Out solutions describe in particular the motion of the…
In this paper we revisit the derivations of model equations describing long nonlinear longitudinal bulk strain waves in elastic rods within the scope of the Murnaghan model in order to derive a Boussinesq-type model, and extend these…
This work studies the stability of solitary waves of a class of sixth-order Boussinesq equations.
One-parameter families of exact two-component solitary-wave solutions for interacting high-frequency (HF) and low-frequency (LF) waves are found in the framework of Zakharov-type models, which couple the nonlinear Schr\"odinger equation…
The present paper is concerned with the existence of solitary wave solutions of Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results of existence of solitary waves of…
We study the fate of internal gravity waves approaching the centre of a non-rotating solar-type star, by performing 3D numerical simulations using a Boussinesq-type model. These waves are excited at the top of the radiation zone by the…
In this paper we deal with the long time existence for the Cauchy problem associated to BBM-type Boussinesq systems of equations which are asymptotic models for long wave, small amplitude gravity surface water waves. As opposed to previous…
To investigate the finite time singularity in three-dimensional (3D) Euler flows, the simplified model of 3D axisymmetric incompressible fluids (i.e., two-dimensional Boussinesq approximation equations) is studied numerically. The system…
The aim of this work is to introduce and analyze a finite element discontinuous Galerkin method on polygonal meshes for the numerical discretization of acoustic waves propagation through poroelastic materials. Wave propagation is modeled by…
Wave propagation in a stratified fluid / porous medium is studied here using analytical and numerical methods. The semi-analytical method is based on an exact stiffness matrix method coupled with a matrix conditioning procedure, preventing…