Related papers: Long wavelength limit for the quantum Euler-Poisso…
We justify rigorously the convergence of the amplitude of solutions of Nonlinear-Schr\"odinger type Equations with non zero limit at infinity to an asymptotic regime governed by the Korteweg-de Vries equation in dimension 1 and the…
In the paper, we consider the Cauchy problem on the spatially one-dimensional Vlasov-Poisson-Landau system modelling the motion of ions under a generalized Boltzmann relation. Let the Knudsen number and the Debye length be given as…
Waves with different symmetries exist in two-component Bose-Einstein condensates (BECs) whose dynamics is described by a system of coupled Gross-Pitaevskii (GP) equations. A first type of waves corresponds to excitations for which the…
It is universally accepted that the cubic, nonlinear Schrodinger equation (NLS) models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves, while the Kortewegde Vries equation (KdV) models the propagation of…
We investigate the existence and properties of traveling waves for the Euler-Korteweg system with general capillarity and pressure. Our main result is the existence in dimension two of waves with arbitrarily small energy. They are obtained…
The Korteweg-de Vries (KdV) equation with periodic boundary conditions is considered. The interaction of a periodic solitary wave (cnoidal wave) with high frequency radiation of finite energy ($L^2$-norm) is studied. It is proved that the…
We consider the one-dimensional ions dynamics in weakly collisional plasmas governed by the Vlasov-Poisson-Landau system under the Boltzmann relation with the small collision frequency $\nu>0$. It is observed in physical experiments that…
In this work, the semi-inverse method has been used to derive the Lagrangian of the Korteweg-de Vries (KdV) equation. Then, the time operator of the Lagrangian of the KdV equation has been transformed into fractional domain in terms of the…
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude ion-acoustic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the…
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic ion-acoustic waves in unmagnitized collisionless weakly relativistic warm plasma. The Lagrangian…
The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. The Lagrangian of the time fractional KdV equation is used in similar form to the…
We consider a system of $N$ bosons confined to a thin waveguide, i.e.\ to a region of space within an $\varepsilon$-tube around a curve in $\mathbb{R}^3$. We show that when taking simultaneously the NLS limit $N\to \infty$ and the limit of…
We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been…
We consider quasilinear generalizations of the Korteweg-de Vries equation and dispersive perturbations of the Euler equations for compressible fluids, either in Lagrangian or in Eulerian coordinates. In particular, our framework includes…
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\e^2$, $\e\ll 1$, is characterized by the appearance of a zone of rapid modulated oscillations. These oscillations are approximately described by…
We consider a Boussinesq equation posed on the infinite periodic necklace graph. For the description of long wave traveling waves we derive the KdV equation and establish the validity of this formal approximation by providing estimates for…
The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact…
Quantum theory and relativity exhibit several formal analogies with fluid mechanics. This paper extends upon known analogies by showing that under specific assumptions, an Euler-Korteweg vortex model can be cast into equations that are…
We study the three dimensional many-particle quantum dynamics in mean-field setting. We forge together the hierarchy method and the modulated energy method. We prove rigorously that the compressible Euler equation is the limit as the…
We consider the Rosenau-Korteweg-de Vries-regularized long wave and Rosenau- Korteweg-de Vries equations, which contain nonlinear dispersive effects. We prove that, as the diffusion parameter tends to zero, the solutions of the dispersive…