Related papers: Interaction of interfacial waves with an external …
The stability and transition in the bottom boundary layer under a solitary wave are analysed in the presence of finite amplitude disturbances. First, the receptivity of the boundary layer is investigated using a linear input-output…
We rigorously study the long time dynamics of solitary wave solutions of the nonlinear Schr\"odinger equation in {\it time-dependent} external potentials. To set the stage, we first establish the well-posedness of the Cauchy problem for a…
A two-dimensional water wave system is examined consisting of two discrete incompressible fluid domains separated by a free common interface. In a geophysical context this is a model of an internal wave, formed at a pycnocline or…
Head-on collisions of ion-acoustic solitary waves in a collisionless plasma consisting of cold ions and Boltzmann electrons are studied using the particle-in-cell simulation. It is shown that the collision of solitary waves can occur under…
Classically, wave interference is a phenomenon that can be explained by considering only the waves themselves, that is, without the need to consider the apparatus that monitors or observes them. Thus, in classical theories, interference can…
The aim of this work is to investigate the interaction of gravity-capillary waves resonantly excited by two moving disturbances along the free surface. The problem is formulated using the full Euler equations and numerical computations are…
We investigate the interaction of solitons with an external periodic field within the framework of the modified Korteweg-de Vries (mKdV) equation. In the case of small perturbation a simple dynamical system is used to describe the soliton…
We study the propagation of solitary waves in a Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with small random heterogeneity in the linear spring force. Perturbed by the random environment, solitary waves lose energy through a radiative tail,…
In this work, we consider the electromechanical density pulse as a coupled solitary waves represented by a longitudinal compression wave and an out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We analyzed using,…
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One…
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. They depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the…
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient…
We analytically compute the long-term orbital variations of a test particle orbiting a central body acted upon by an incident monochromatic plane gravitational wave. We assume that the characteristic size of the perturbed two-body system is…
A two-component Bose-Einstein condensate that is confined in a one-dimensional ring potential supports solitary-wave solutions, which we evaluate analytically. The derived solutions are shown to be unique. The corresponding dispersion…
The exchange of energy between a classical open system and its environment can be analysed for a single run of an experiment using the phase space trajectory of the system. By contrast, in the quantum regime such energy exchange processes…
When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to…
The solitary waves are investigated through the Bernstein-Greene-Kruskal integral method with the ion response. We consider two specific cases of ions, i.e., the single stream with the waterbag distribution and the two counter-propagating…
In this paper we examine the stability of scalar perturbations in nonsingular models which emerge from an interacting vacuum component. The analysis developed in this paper relies on two phenomenological choices for the energy exchange…
We study asymptotic stability of solitary wave solutions in the one-dimensional Benney-Luke equation, a formally valid approximation for describing two-way water wave propagation. For this equation, as for the full water wave problem, the…
Some effects of surface tension on fully-nonlinear, long, surface water waves are studied by numerical means. The differences between various solitary waves and their interactions in subcritical and supercritical surface tension regimes are…