相关论文: Solitary wave collisions for Whitham-Boussinesq sy…
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 note we study solitary wave solutions of a class of Whitham-Boussinesq systems which includes the bi-directional Whitham system as a special example. The travelling wave version of the evolution system can be reduced to a single…
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.…
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…
A coupled BBM system of equations is studied in the situation of water waves propagating over decreasing fluid depth. A conservation equation for mass and a wave breaking criterion valid in the Boussinesq approximation is found. A Fourier…
Using numerical modeling investigated interaction of solitary waves (solitons) of the regularized long wave equation. For reception the stable model of the nonlinear medium are used methods of the linear prediction and progressive…
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…
Recently, two different proofs for large and intermediate-size solitary waves of the nonlocally dispersive Whitham equation have been presented, using either global bifurcation theory or the limit of waves of large period. We give here a…
Weakly-nonlinear waves in a layered waveguide with an imperfect interface (soft bonding between the layers) can be modelled using coupled Boussinesq equations. We assume that the materials of the layers have close mechanical properties, in…
The possible solitary wave solutions for a general Boussinesq (GBQ) type fluid model are studied analytically. After proving the non-Painlev\'e integrability of the model, the first type of exact explicit travelling solitary wave with a…
This article presents a numerical investigation of overtaking collisions between two solitary waves in the context of the Schamel equation. Our study reveals different regimes characterized by the behavior of the wave interactions. In…
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…
In this paper we consider the decay rate of solitary-wave solutions to some classes of non-linear and non-local dispersive equations, including for example the Whitham equation and a Whitham--Boussinesq system. The dispersive term is…
The existence of multi-speed solitary waves for the one-dimensional good Boussinesq equation with a power nonlinearity is proven. These solutions are shown to behave at large times as a pair of scalar solitary waves traveling at different…
In this paper, we employ the bifurcation theory of planar dynamical systems to investigate the travelling-wave solutions to a dual equation of the Kaup-Boussinesq system. The expressions for smooth solitary-wave solutions are obtained.
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 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…
Systems of solitary-waves in the 1D Gross-Pitaevskii equation, which models a trapped atomic Bose-Einstein condensate, are investigated theoretically. To analyse the soliton-like nature of these solitary-waves, a particle analogy for the…
It is an open fundamental question how the classical appearance of our environment arises from the underlying quantum many-body theory. We propose that phenomena involved in the quantum-to-classical transition can be probed in collisions of…
In the study, the collocation method based on exponential cubic B-spline functions is proposed to solve one dimensional Boussinesq systems numerically. Two initial boundary value problems for Regularized and Classical Boussinesq systems…