相关论文: Hexagonal standing wave patterns of a two-dimensio…

We construct three-dimensional families of small-amplitude gravity-driven rotational steady water waves on finite depth. The solutions contain counter-currents and multiple crests in each minimal period. Each such wave generically is a…

In this paper we deal with two dimensional cubic Dirac equations appearing as effective model in gapped honeycomb structures. We give a formal derivation starting from cubic Schr\"odinger equations and prove the existence of standing waves…

In this paper, the closed-form analytic solutions of two new Faraday's standing solitary waves due to the parametric resonance of liquid in a vessel vibrating vertically with a constant frequency are given for the first time. Using a model…

In this paper, we study various dissipative mechanics associated with the Boussinesq systems which model two-dimensional small amplitude long wavelength water waves. We will show that the decay rate for the damped one-directional model…

The travelling wave problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system firstly appeared in [Dinvay, Dutykh, Kalisch 2018], where it was numerically shown to be stable and…

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…

A century and a half ago, J. Boussinesq derived an equation for the propagation of water waves in a channel. Despite the fundamental importance of this equation for a number of physical phenomena, mathematical results on it remain scarce.…

We prove the existence on long time scales of the solutions to the Cauchy problem for a version of weakly transverse Boussinesq systems arising in the modeling of surface water waves. This system is much more complicated than the isotropic…

We study here some asymptotic models for the propagation of internal and surface waves in a two-fluid system. We focus on the so-called long wave regime for one dimensional waves, and consider the case of a flat bottom. Starting from the…

In this paper, we study the generalized Boussinesq equation as a model for the water wave problem with surface tension. Initially, we investigate the initial value problem within Sobolev spaces, deriving conditions under which solutions are…

The initial-value problem for a particular bidirectional Whitham system modelling surface water waves is under consideration. This system was recently introduced in [4]. It is numerically shown to be stable and a good approximation to the…

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…

In this paper, we investigate the well-posedness of a nonlinear dispersive model with variable coefficients that describes the evolution of surface waves propagating through a one-dimensional shallow water channel of finite length with…

We derive and analyze in the framework of the mild-slope approximation a new double-layer Boussinesq-type model which is linearly and nonlinearly accurate up to deep water. Assuming the flow to be irrotational, we formulate the problem in…

The aim of this paper is to establish the existence of solitary wave solutions for two classes of two-layers systems modeling the propagation of internal waves. More precisely we will consider the Boussinesq-Full dispersion system and the…

In this paper the permanent profile waves governed by a Boussinesq-type wave equation are analysed. The model involves displacement-type nonlinearities and dispersion terms. Physically such a model equation describes longitudinal waves…

In this note, we prove local-in-time well-posedness for a fully dispersive Boussinesq system arising in the context of free surface water waves in two and three spatial dimensions. Those systems can be seen as a weak nonlocal dispersive…

In this paper we are concerned with a nonlocal system to model the propagation of internal waves in a two-layer interface problem with rigid lid assumption and under a Boussinesq regime for both fluids. The main goal is to investigate…

In this paper, we establish the existence and instability of standing wave for a system of nonlinear Schr\"{o}dinger equations arising in the two-wave model with quadratic interaction in higher space dimensions under mass resonance…

We study the behavior of shallow water waves propagating over bathymetry that varies periodically in one direction and is constant in the other. Plane waves traveling along the constant direction are known to evolve into solitary waves, due…