Related papers: Evolution of perturbed long nonlinear plane, ring …
In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov…
We consider a system of equations for the description of nonlinear waves in a liquid with gas bubbles. Taking into account high order terms with respect to a small parameter, we derive a new nonlinear partial differential equation for the…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
In this work, we investigate non-classical wavetrain formations, and particularly dispersive shock waves (DSWs), or undular bores, in systems exhibiting non-convex dispersion. Our prototypical model, which arises in shallow water wave…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
The two-dimensional cubic nonlinear Schrodinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional…
In this work, we study numerically the temporal evolution of an initially random large-scale velocity field under governed by the hyperviscous incompressible Navier-Stoke equations. Three stages are clearly observed during the evolution.…
In this paper, we study the novel nonlinear wave structures of a (2+1)-dimensional variable-coefficient Korteweg-de Vries (KdV) system by its analytic solutions. Its $N$-soliton solution are obtained via Hirota's bilinear method, and in…
A numerical study of the 2D Amick-Schonbek Boussinesq system is presented. Numerical evidence is given for the transverse stability of the 1D solitary waves that are line solitary waves of the 2D equations. It is shown that initial data not…
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…
We show existence and uniqueness of strong solutions to a Navier-Stokes/Cahn-Hilliard type system on a given two-dimensional evolving surface in the case of different densities and a singular (logarithmic) potential. The system describes a…
A general Hamiltonian wave system with quartic resonances is considered, in the standard kinetic limit of a continuum of weakly interacting dispersive waves with random phases. The evolution equation for the multimode characteristic…
By using the long-wave approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a B\'enard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it can…
We consider the evolution of contact lines for thermal convection of viscous fluids in a 2D open-top vessel. The domain is bounded above by a free moving boundary and otherwise by the solid wall of a vessel. The dynamics of the fluid are…
Travelling and rotating waves are ubiquitous phenomena observed in time dependent PDEs modelling the combined effect of dissipation and non-linear interaction. From an abstract viewpoint they appear as relative equilibria of an equivariant…
Integrable two-dimensional models which possess an integral of motion cubic or quartic in velocities are governed by a single prepotential, which obeys a nonlinear partial differential equation. Taking into account the latter's invariance…
Instabilities driven by strong gradients appear in a wide variety of physical systems, including plasmas, neutral fluids, and self-gravitating systems. This work develops an analytic formulation to describe the transport structure and…
A Boussinesq system for a non-linear shallow water is considered. The nonlinear and topological effects are examined through an associated matrix spectral problem. It is shown an equivalence relationship between the bound states and…
We study the existence and numerical computation of traveling wave solutions for a family of nonlinear higher-order Boussinesq evolution systems with a Hamiltonian structure. This general Boussinesq evolution system includes a broad class…
The two-dimensional solitary waves of the Gross-Pitaevskii equation in the Kadomtsev-Petviashvili limit are unstable with respect to three-dimensional perturbations. We elucidate the stages in the evolution of such solutions subject to…