Related papers: An Algebraic Derivation of the Standing Wave Probl…
The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…
Propagation of unsteady waves under the effect of a step point load on a square lattice of spring-connected masses is investigated. The problem is solved by two methods. Asymptotic solutions at large time intervals, which describe the…
Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudo-differential equation, involving a periodic…
There have been several existence results for the standing waves of FitzHugh-Nagumo equations. Such waves are the connecting orbits of an autonomous second-order Lagrangian system and the corresponding kinetic energy is an indefinite…
We consider solutions in frequency bands of dispersive equations on the line defined by Fourier multipliers, these solutions being considered as wave packets. In this paper, a refinement of an existing method permitting to expand…
Orbital stability property for weakly coupled nonlinear Schr\"odinger equations is investigated. Different families of orbitally stable standing waves solutions will be found, generated by different classes of solutions of the associated…
The periodic standing wave method studies circular orbits of compact objects coupled to helically symmetric standing wave gravitational fields. From this solution an approximation is extracted for the strong field, slowly inspiralling…
In the present work, we explore the possibility of developing rogue waves as exact solutions of some nonlinear dispersive equations, such as the nonlinear Schr\"odinger equation, but also, in a similar vein, the Hirota, Davey-Stewartson,…
It is demonstrated that a standard coupled-mode theory can successfully describe weakly-nonlinear gravity water waves in Bragg resonance with a periodic one-dimensional topography. Analytical solutions for gap solitons provided by this…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear…
We continue the study for standing wave solutions of $abcd$-systems which was started by Chen and Iooss \cite{chen2005standing} for the BBM system via the Lyapunov-Schmidt method. In this paper, we will first discuss the feasibility of the…
For a class of scalar partial differential equations that incorporate convection, diffusion, and possibly dispersion in one space and one time dimension, the stability of traveling wave solutions is investigated. If the initial perturbation…
A nonlinear Schr\"odinger equation with repulsive (defocusing) nonlinearity is considered. As an example, a system with a spatially varying coefficient of the nonlinear term is studied. The nonlinearity is chosen to be repelling except on a…
We establish via variational methods the existence of a standing wave together with an estimate on the convergence to its asymptotic states for a bistable system of partial differential equations on a periodic domain. The main tool is a…
We report on the experimental study of axisymmetric gravity-capillary standing waves generated by a vertically vibrating ring partially immersed into a fluid. Different regimes of standing waves are highlighted at the basin center depending…
We study the instability of standing-wave solutions $e^{i\omega t}\phi_{\omega}(x)$ to the inhomogeneous nonlinear Schr\"{o}dinger equation $$i\phi_t=-\triangle\phi+|x|^2\phi-|x|^b|\phi|^{p-1}\phi, \qquad \in\mathbb{R}^N, $$ where $ b > 0 $…
Wave propagation in curved tubular domains is considered. A general version of Webster's equation is derived from the scattering passive wave equation. More precisely, it is shown that planar averages of a sufficiently smooth solution of…
This work comes as the second part in a series of investigations into the dynamics of rotating waves as solutions to lattice dynamical systems. Such nonlinear waves as solutions to mathematical equations are of great interest throughout the…
Fractional wave equation arises in different type of physical problems such as the vibrating strings, propagation of electro-magnetic waves, and for many other systems. The exact analytical solution of the fractional differential equation…