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In this paper we derive a higher-order KdV equation (HKdV) as a model to describe the unidirectional propagation of waves on an internal interface separating two fluid layers of varying densities. Our model incorporates underlying currents…
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…
We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain…
The theory of 3-layer density stratified ideal fluids is examined with a view towards its generalization to the n-layer case. The focus is on structural properties, especially for the case of a rigid upper lid constraint. We show that the…
In this paper we consider the Benjamin equation, a partial differential equation that models one-way propagation of long internal waves of small amplitude along the interface of two fluid layers under the effects of gravity and surface…
We provide a consistent statistical-mechanical treatment for describing the thermodynamics and the structure of fluids embedded in the hyperbolic plane. In particular, we derive a generalization of the virial equation relating the bulk…
We study asymptotic reductions and solitary waves of a weakly nonlocal defocusing nonlinear Schr\"odinger (NLS) model. The hydrodynamic form of the latter is analyzed by means of multiscale expansion methods. To the leading-order of…
The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…
We study the relation between the periodic Benjamin-Ono equation with discrete Laplacian and the two dimensional Toda hierarchy. We introduce the tau-functions tau_pm(z) for the periodic Benjamin-Ono equation, construct two families of…
Self-similar solutions of the so called Airy equations, equivalent to the dispersionless nonlinear Schr\"odinger equation written in Madelung coordinates, are found and studied from the point of view of complete integrability and of their…
The Whitham approach is a well-studied method to describe non-linear integrable systems. Although approximate in nature, its results may predict rather accurately the time evolution of such systems in many situations given initial…
The nonlinear two-dimensional problem, describing periodic steady waves on water of finite depth is considered in the absence of surface tension. It is reduced to a single pseudo-differential operator equation (Babenko's equation), which is…
A thermodynamic analysis of weakly nonlocal non-relativistic fluids is presented under the assumption that an additional scalar field also contributes to the dynamics. The most general evolution of this field and the constitutive relations…
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…
We study the interaction of suitable small and high frequency waves evolving by the flow of the Benjamin-Ono equation. As a consequence, we prove that the flow map of the Benjamin-Ono equation can not be uniformly continuous on bounded sets…
We derive a hydrodynamical description of the eigenvalues of the chiral Dirac spectrum in the vacuum and in the large $N$ (volume) limit. The linearized hydrodynamics supports sound waves. The stochastic relaxation of the eigenvalues is…
We propose a novel dispersive regularization framework for the numerical simulation of the one-dimensional shallow water equations (SWE). The classical hyperbolic system is regularized by a third-order dispersive term in the momentum…
Shallow water waves phenomena in nature attract the attention of scholars and play an important role in fields such as tsunamis, tidal waves, solitary waves, and hydraulic engineering. Hereby,…
This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and ions, through a set of scaling limits.…
In this work we presented a derivation of the quantum hydrodynamic equations for neutral bosons. We considered short range interaction between particles. This interaction consist binary interaction $U(\textbf{r}_{i},\textbf{r}_{j})$ and…