相关论文: Cosmology and the Korteweg-de Vries Equation

In this paper we review the physical relevance of a Korteweg-de Vries (KdV) equation with higher-order dispersion terms which is used in the applied sciences and engineering. We also present exact traveling wave solutions to this…

The Korteweg-de Vries equation (KdV) and various generalized, most often semi- linear versions have been studied for about 50 years. Here, the focus is made on a quasi-linear generalization of the KdV equation, which has a fairly general…

This manuscript embarks on an in-depth exploration of the modified Korteweg-de Vries (mKdV) equation, with a particular emphasis on unraveling the intricate structure of its infinite symmetries and their physical interpretations. Central to…

Generalized solitary waves with exponentially small non-decaying far field oscillations have been studied in a range of singularly-perturbed differential equations, including higher-order Korteweg-de Vries (KdV) equations. Many of these…

With the nonuniform media taken into account, the nonisospectral and variable-coefficient Korteweg-de Vries equation, which describes various physical situations such as fluid dynamics and plasma, is under investigation in this paper. With…

In a previous work, assuming that the nucleus can be treated as a perfect fluid, we have studied the propagation of perturbations in the baryon density. For a given equation of state we have derived a Korteweg - de Vries (KdV) equation from…

All solutions of the Korteweg -- de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that…

The KdV equation is a model equation for waves at the surface of an inviscid incompressible fluid, and it is well known that the equation describes the evolution of unidirectional waves of small amplitude and long wavelength fairly…

We study the dynamics of multi-component Bose gas described by the Vector Nonlinear Schr\"{o}dinger Equation (VNLS), aka the Vector Gross--Pitaevskii Equation (VGPE) . Through a Madelung transformation, the VNLS can be reduced to coupled…

We show how to apply ideas from the theory of rough paths to the analysis of low-regularity solutions to non-linear dispersive equations. Our basic example will be the one dimensional Korteweg--de Vries (KdV) equation on a periodic domain…

In this paper, nonlocal symmetries and exact solutions of variable coefficient Korteweg-de Vries (KdV) equation are studied for the first time. Using pseudo-potential, high order nonlocal symmetries of time-dependent coefficient KdV…

The letter is a response to the recent article by J. Lidsey. We demonstrate that the Schwarzian derivative technique developed therein is but a consequence of linearizabiliy of the original cosmological equations. Furthermore, we show the…

We present a noncommutative extension of Quantum Cosmology and study the Kantowski-Sachs (KS) cosmological model requiring that the two scale factors of the KS metric, the coordinates of the system, and their conjugate canonical momenta do…

The evolution of a solitary wave with very weak nonlinearity which was originally investigated by Miles [4] is revisited. The solution for a one-dimensional gravity wave in a water of uniform depth is considered. This leads to finding the…

In this letter, we derive the Korteweg-de Vries (KdV) equation corresponding to the surface dynamics of a shallow depth ($h$) two-dimensional fluid with odd viscosity ($\nu_o$) subject to gravity ($g$) in the long wavelength weakly…

We consider solutions of the generalized Korteweg-de Vries equations (gKdV) which are non dispersive in some sense (in the spirit of [18]) and which remain close to multi-solitons. We show that these solutions are necessarily pure…

Uniform estimates for the decay structure of the $n$-soliton solution of the Korteweg-deVries equation are obtained. The KdV equation, linearized at the $n$-soliton solution is investigated in a class $\WW$ consisting of sums of travelling…

The Korteweg-de Vries (KdV) equation governs the propagation of nonlinear internal and surface gravity waves in shallow ocean environments, where the balance between nonlinear steepening and frequency-dependent dispersion produces solitons.…

Some types of coupled Korteweg de-Vries (KdV) equations are derived from an atmospheric dynamical system. In the derivation procedure, an unreasonable $y$-average trick (which is usually adopted in literature) is removed. The derived models…

There is a well explored relationship between quantum mechanical scattering from a potential and the Korteweg-de Vries (KdV) equation of fluid dynamics: if the potential is 'evolved' according to the KdV equation then it will have the same…