相关论文: Removing trailing tails and delays induced by arti…
Compactons are compactly supported solitary waves for nondissipative evolution equations with nonlinear dispersion. In applications, these model equations are accompanied by dissipative terms which can be treated as small perturbations. We…
We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Pad\'e approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order…
A numerical study of the nonlinear wave solutions of the Rosenau-Pikovsky K(cos) equation is presented. This equation supports at least two kind of solitary waves with compact support: compactons of varying amplitude and speed, both…
The focal point of this paper is to theoretically investigate and numerically validate the effect of time delay on the exponential stabilization of a class of coupled hyperbolic systems with delayed and non-delayed dampings. The class in…
We study the properties of compacton-anticompacton collision processes. We compare and con- trast results for the case of compacton-anticompacton solutions of the K(l, p) Rosenau-Hyman (RH) equation for l = p = 2, with…
Extending a Pade approximant method used for studying compactons in the Rosenau-Hyman (RH) equation, we study the numerical stability of single compactons of the Cooper-Shepard-Sodano (CSS) equation and their pairwise interactions. The CSS…
(Abbreviated) We investigate the dynamical mechanisms responsible for producing tidal tails from dwarf satellites using N-body simulations. We identify two important dynamical co-conspirators: 1) the points where the attractive force of the…
The periodic standing-wave method for binary inspiral computes the exact numerical solution for periodic binary motion with standing gravitational waves, and uses it as an approximation to slow binary inspiral with outgoing waves. Important…
This report is a review of Darwin's classical theory of bodily tides in which we present the analytical expressions for the orbital and rotational evolution of the bodies and for the energy dissipation rates due to their tidal interaction.…
The authors consider non-autonomous dynamical behavior of wave-type evolutionary equations with nonlinear damping and critical nonlinearity. These type of waves equations are formulated as non-autonomous dynamical systems (namely,…
In this paper we are consider radiating solitary wave solutions of coupled regularised Boussinesq equations. This type of solution consists of a leading solitary wave with a small-amplitude co-propagating oscillatory tail, and emerges from…
This paper addresses the analysis and numerical assessment of a computational method for solving the Cahn--Hilliard equation defined on a surface. The proposed approach combines the stabilized trace finite element method for spatial…
Stability is an important aspect of numerical methods for hyperbolic conservation laws and has received much interest. However, continuity in time is often assumed and only semidiscrete stability is studied. Thus, it is interesting to…
We investigate the dissipative dynamics of linear and nonlinear waves in harmonic traps by means of engineered complex non-Hermitian potentials. By combining an analytical mapping between real and complex Schr\"odinger equations with direct…
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.…
For a one-dimensional smooth vector field in a neighborhood of an unstable equilibrium, we consider the associated dynamics perturbed by small noise. We give a revealing elementary proof of a result proved earlier using heavy machinery from…
The light damping hypothesis is usually assumed in structural dynamics since dissipative forces are in general weak with respect to inertial and elastic forces. In this paper a novel numerical method of time integration based on the…
The relevance of perturbed forms of the Korteweg-de Vries equation to a range of physical problems is discussed. Solutions which are perturbations of solitary travelling wave solutions are then considered, focussing predominantly on the…
We apply the homotopy perturbation method to construct series solutions for the fractional Rosenau-Hyman (fRH) equation and study their dynamics. Unlike the classical RH equation where compactons arise from truncated periodic solutions, we…
This paper presents a new theory of the dynamical tides of celestial bodies. It is founded on a Newtonian creep instead of the classical delaying approach of the standard viscoelastic theories and the results of the theory derive mainly…