相关论文: An analytical proof for the stability of Heimburg-…
The $abcd$-Boussinesq system is a model of two equations that can describe the propagation of small-amplitude long waves in both directions in the water of finite depth. Considering the Hamiltonian regimes, where the parameters $b$ and $d$…
This work studies the stability of solitary waves of a class of sixth-order Boussinesq equations.
Boussinesq-type wave equations involve nonlinearities and dispersion. In this paper a Boussinesq-type equation with amplitude-dependent nonlinearities is presented. Such a model was proposed by Heimburg and Jackson (2005) for describing…
The aim of this paper is to present a survey and a detailed numerical study on a remarkable Boussinesq system describing weakly nonlinear, long surface water waves. In the one-dimensional case, this system can be viewed as a dispersive…
Primarily motivated by the stability analysis of nonlinear waves in second-order in time Hamiltonian systems, in this paper we develop an instability index theory for quadratic operator pencils acting on a Hilbert space. In an extension of…
The question for linear stability of spatially periodic waves for the Boussinesq equation (the cases $p=2,3$) and the Klein-Gordon-Zakharov system is considered. For a wide class of solutions, we completely and explicitly characterize their…
New results concerning the orbital stability of periodic traveling wave solutions for the "abcd" Boussinesq model will be shown in this manuscript. For the existence of solutions, we use basic tools of ordinary differential equations to…
This paper studies the orbital stability of solitary waves for the following Schr\"{o}dinger-Boussinesq system \begin{equation*} \begin{cases} { \begin{array}{ll} i\varepsilon_t+\varepsilon_{xx}=n\varepsilon+\gamma…
We examine the stability of a class of solitons, obtained from a generalization of the Boussinesq equation, which have been proposed to be relevant for pulse propagation in biomembranes and nerves. These solitons are found to be stable with…
The theory of internal waves between two layers of immiscible fluids is important both for its applications in oceanography and engineering, and as a source of interesting mathematical model equations that exhibit nonlinearity and…
We consider the generalized Good-Boussinesq model in one dimension, with power nonlinearity and data in the energy space $H^1\times L^2$. This model has solitary waves with speeds $-1<c<1$. When $|c|$ approaches 1, Bona and Sachs showed…
The general form of the cubic Boussinesq-type equation is considered. In special cases, this equation is reduced to the three different versions of the cubic Boussinesq equations and also the generalized modified cubic Boussinesq equation.…
In this article we are concerned with the instability and stability properties of traveling wave solutions of the double dispersion equation $~u_{tt} -u_{xx}+a u_{xxxx}-bu_{xxtt} = - (|u|^{p-1}u)_{xx}~$ for $~p>1$, $~a\geq b>0$. The main…
We consider the generalized Good-Boussinesq (GB) model in one dimension, with subcritical power nonlinearity $1<p<5$ and data in the energy space $H^1\times L^2$. This model has solitary waves with speeds $c\in (-1,1)$. If…
A regularized Boussinesq equation is studied as a dispersive, long-wave (quasicontinuum) approximation of the Fermi-Pasta-Ulam lattice with a general cubic interaction force. Explicit periodic traveling wave solutions in terms of Jacobi…
We develop a general theory for linear stability of traveling waves of second order in time PDE's. More precisely, we introduce an explicitly computable index $\om^*\in (0, \infty]$ (depending on the self-adjoint part of the linearized…
This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…
Consideration is given to three different full dispersion Boussinesq systems arising as asymptotic models in the bi-directional propagation of weakly nonlinear surface waves in shallow water. We prove that, under a non-cavitation condition…
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq-Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on…
In this paper a three-parameter family of Boussinesq systems is studied. The systems have been proposed as models of the propagation of long internal waves along the interface of a two-layer system of fluids with rigid-lid condition for the…