Related papers: Phase modulated solitary waves controlled by botto…
The work presented here emanates from questions arising from experimental observations of the propagation of surface water waves. The experiments in question featured a periodically moving wavemaker located at one end of a flume that…
We study the behavior of solitary-wave solutions of some generalized nonlinear Schr\"odinger equations with an external potential. The equations have the feature that in the absence of the external potential, they have solutions describing…
This paper is concerned with a class of partial differential equations, which are the linear combinations, with constant coefficients, of the classical flows of the KdV hierarchy. A boundary value problem with inhomogeneous boundary…
The diffraction of a plane wave by a transversely inhomogeneous isotropic nonmagnetic linearly polarized dielectric layer filled with a Kerr-type nonlinear medium is considered. The analytical and numerical solution techniques are…
Our aim is to study the effect of a continuous prescribed density variation on the propagation of ocean waves. More precisely, we derive KdV-type shallow water model equations for unidirectional flows along the Equator from the full…
Fully localised solitary waves are travelling-wave solutions of the three-dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of…
We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV…
We consider the stabilization problem on a manifold with boundary for a wave equation with measure-valued linear damping. For a wide class of measures, containing Dirac masses on hypersurfaces as well as measures with fractal support, we…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
A closed-form analytical solution is found for the nonlinear dynamics of isolated, near-threshold waves in the presence of strong scattering. The proposed solution can be useful in verifying codes across several disciplines, including…
A degenerate wave equation with time-varying delay in the boundary control input is considered. The well-posedness of the system is established by applying the semigroup theory. The boundary stabilization of the degenerate wave equation is…
We prove that if a solution of an equation of KdV type is bounded above by a traveling wave with an amplitude that decays faster than a given linear exponential then it must be zero. We assume no restrictions neither on the size nor in the…
We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class…
A single incompressible, inviscid, irrotational fluid medium bounded by a free surface and varying bottom is considered. The Hamiltonian of the system is expressed in terms of the so-called Dirichlet-Neumann operators. The equations for the…
We investigate the existence and the singular structure of delta wave solutions to a semilinear strictly hyperbolic equation with strongly singular initial and boundary conditions. The boundary conditions are given in nonlocal form with a…
The evolution of the amplitude of two nonlinearly interacting waves is considered, via a set of coupled nonlinear Schroedinger-type equations. The dynamical profile is determined by the wave dispersion laws (i.e. the group velocities and…
In this paper we establish several results on approximate controllability of a semilinear wave equation by making use of a single multiplicative control. These results are then applied to discuss the exact controllability properties for the…
In this paper, we consider a weakly coupled system consisting of a viscoelastic Kirchhoff plate equation involving free boundary conditions and the viscoelastic wave equation with Dirichlet boundary conditions in a bounded domain. By…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
Effects of nonlinear dynamics of solitary waves and wave modulations within the modular (also known as quadratically cubic) Korteweg - de Vries equation are studied analytically and numerically. Large wave events can occur in the course of…