This presentation discusses different Zakharenko waves (ZWs) such as the non-dispersive ZWs, dispersive leaky ZWs, slow surface ZWs and ultrasonic surface ZWs, as well as their possible applications. The nondispersive Zakharenko waves can be found in complex systems such as different layered and quantum systems. Existence examples of the non-dispersive Zakharenko waves in both fundamental modes...

Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized ...

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov-type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...

Heat transfer enhancements are investigated inside channels by controlling thermal dispersion effects inside the fluid. Different distributions for the dispersive elements such as nanoparticles or flexible hairy fins extending from the channel plates are considered. Energy equations for different fluid regions are dimensionalized and solved analytically and numerically. The boundary arrangement...

The nonlinear propagation of optical pulses in dielectric waveguides and resonators provides a laboratory to investigate a wide range of remarkable interactions. Many of the resulting phenomena find applications in optical systems. One example is dispersive wave generation, the optical analog of Cherenkov radiation. These waves have an essential role in fiber spectral broadeners that are routin...

We analyze a quantum trajectory model given by a steady-state hydrodynamic system for quantum fluids with positive constant temperature in bounded domains for arbitrary large data. The momentum equation can be written as a dispersive thirdorder equation for the particle density where viscous effects are incorporated. The phenomena that admit positivity of the solutions are studied. The cases, o...

The paper describes a new approach to global smoothing problems for dispersive and non-dispersive evolution equations based on the global canonical transforms and the underlying global microlocal analysis. For this purpose, the Egorov–type theorem is established with canonical transformations in the form of a class of Fourier integral operators, and their weighted L–boundedness properties are d...

We consider two physically and mathematically distinct regularization mechanisms of scalar hyperbolic conservation laws. When the flux is convex, the combination of di↵usion and dispersion are known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-di↵usion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A r...

When posed on a periodic domain in one space variable, linear dispersive evolution equations with integral polynomial dispersion relations exhibit strikingly different behaviors depending upon when the time is rational or irrational relative to the length of the interval: the Talbot phenomenon of dispersive quantization and fractalization. The purpose of this paper is to show that these phenome...

The fully nonlinear and weakly dispersive Green–Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed, which could be adapted to many physical models that are dispersive corrections of hyperbolic system...