相关论文: Weak Asymptotics of Shock Wave Formation Process

When traditional linearised theory is used to study gravity-capillary waves produced by flow past an obstruction, the geometry of the object is assumed to be small in one or several of its dimensions. In order to preserve the nonlinear…

A weak asynchronous system is a trace monoid with a partial action on a set. A polygonal morphism between weak asynchronous systems commutes with the actions and preserves the independence of events. We prove that the category of weak…

We develop an analytic theory to describe spiral density waves propagating in a shearing disc in the weakly nonlinear regime. Such waves are generically found to be excited in simulations of turbulent accretion disks, in particular if said…

We have used an extension of our slow light technique to provide a method for inducing small density defects in a Bose-Einstein condensate. These sub-resolution, micron-sized defects evolve into large amplitude sound waves. We present an…

The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point $t_*$ and fast oscillating behavior after the point $t_*$. In the transition layer the behavior of the…

For the one-dimensional case, we establish the long-time asymptotics of solution to Cauchy problem and prove existence of modified wave operators. In particular, we show that the part of the wave travels ballistically if the potential is…

Shockwaves are violent nonlinear distortions of wave motion which have been reported in fluid waves and electromagnetic waves, while here we reveal that a shockwave can occur even in the quantum wave function of a single particle.…

A theoretical study on the weak scattering formulation for flexural waves in thin elastic plates loaded by point-like resonators is reported. Our approach employs the Born approximation and far-field asymptotics of the Green function to…

There has been significant recent interest in the study of water waves coupled with non-zero vorticity. We derive analytical approximations for the exponentially-small free-surface waves generated in two-dimensions by one or several…

Shock waves are an ubiquitous feature of hydrodynamic theories. Given that fermionic quantum many-body systems admit hydrodynamical descriptions on length scales large compared to the Fermi wavelength, it is natural to ask what the status…

We consider a system of nonlinear equations which can be reduced to a degenerate parabolic equation. In the case $x\in\bR^2$ we obtained necessary conditions for the existence of a weakly singular solution of heat wave type…

Steady and unsteady linearised flow past a submerged source are studied in the small-surface-tension limit, in the absence of gravitational effects. The free-surface capillary waves generated are exponentially small in the surface tension,…

The formulation of a canonical deep-water breaking wave problem is introduced, and the results of a set of three-dimensional numerical simulations for deep-water breaking waves are presented. In this paper fully nonlinear progressive waves…

We prove existence of weak solutions to the obstacle problem for semilinear wave equations (including the fractional case) by using a suitable approximating scheme in the spirit of minimizing movements. This extends the results in [9],…

Resonantly forced spiral waves in excitable media drift in straight-line paths, their rotation centers behaving as point-like objects moving along trajectories with a constant velocity. Interaction with medium boundaries alters this…

A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical…

First, a misconception about the spectrum of a confined particle is evidentiated. Then, the results are shown to be incorrect by means of a counter-example, an explicit preparation for the probe is given that yields an arbitrary…

n a number of papers it was shown that there are one-dimensional systems such that they contain solutions with, so called, overcompressive singular shock waves besides the usual elementary waves (shock and rarefaction ones as well as…

We study the Cauchy problem for a kinetic equation arising in the weak turbulence theory for the cubic nonlinear Schr\"odinger equation. We define suitable concepts of weak and mild solutions and prove local and global well posedness…

We consider evolution of wave pulses with formation of dispersive shock waves in framework of fully nonlinear shallow-water equations. Situations of initial elevations or initial dips on the water surface are treated and motion of the…