相关论文: Weak Asymptotics of Shock Wave Formation Process

An asymptotic theory is developed to generate equations that model the global behaviour of electromagnetic waves in periodic photonic structures when the wavelength is not necessarily long relative to the periodic cell dimensions;…

We prove a stable shock formation result for a large class of systems of quasilinear wave equations in two spatial dimensions. We give a precise description of the dynamics all the way up to the singularity. Our main theorem applies to…

In this paper a diffuse-interface model featuring phase change, transition to supercritical conditions, thermal conduction, compressibility effects and shock wave propagation is exploited to deal with the dynamics of a cavitation bubble. At…

We analyze the shock formation process for the 3d non-isentropic Euler equations with the ideal gas law, in which sounds waves interact with entropy waves to produce vorticity. Building on our theory for isentropic flows in [3,4], we give a…

In this Letter, weak turbulence theory is used to investigate interactions among Alfven waves and fast and slow magnetosonic waves in collisionless low-beta plasmas. The wave kinetic equations are derived from the equations of…

Freak waves, or rogue waves, are one of the fascinating manifestations of the strength of nature. These devastating walls of water appear from nowhere, are short-lived and extremely rare. Despite the large amount of research activities on…

In quantum theory particles are represented as wave packets. Shock wave analysis of quantum equations of motion shows that wave function representation in general and wave packet description in particular contains discontinuities due to a…

We consider a mechanism of generation of huge waves by multi-soliton resonant interactions. A non-stationary wave amplification phenomenon is found in some exact solutions of the Kadomtsev-Petviashvili (KP) equation. The mechanism proposed…

We present a scaling technique which transforms the evolution problem for a nonlinear wave equation with small initial data to a linear wave equation with a distributional source. The exact solution of the latter uniformly approximates the…

An asymptotic expansion with respect to a small parameter of a singularly perturbed system of hyperbolic equations, describing vibrations of two rigidly connected strings is constructed. Under certain conditions imposed on these problems,…

Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…

The main result of this work is the construction of multi-solitons solutions that is to say solutions that are time asymptotics to a sum of decoupling solitary waves for the full water waves system with surface tension.

For single and twochannel nucleon-nucleon scattering the asymptotic form of the phase function for r->0 were taken into account for the asymptotic behavior of the wave function. Asymptotics of the wave function will not r^(l+1), and will…

Quasi two-dimensional pattern forming systems with spontaneously broken isotropy represent a novel symmetry class, that is experimentally accessible in electroconvection of homeotropically aligned liquid crystals. We present a weakly…

We study a very general class of first-order linear hyperbolic systems that both become weakly hyperbolic and contain lower-order coefficients that blow up at a single time $t = 0$. In "critical" weakly hyperbolic settings, it is well-known…

An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. Exact solution with own angular momentum in form of a…

The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We present the main techniques which are required to apply the…

An effective surface equation, that encapsulates the detail of a microstructure, is developed to model microstructured surfaces. The equations deduced accurately reproduce a key feature of surface wave phenomena, created by periodic…

When a planar shock wave interacts with a random pattern of pre-shock density non-uniformities, it generates an anisotropic turbulent velocity/vorticity field. This turbulence plays an important role at the early stages of the mixing…

A model of steady-state X-shaped wave generation by a superluminal (supersonic) pointlike source infinitely moving along a straight line is extended to a more realistic causal scenario of a source pulse launched at time zero and propagating…