Dispersive shock waves
http://www.scholarpedia.org/article/Dispersive_shock_waves WebA detailed numerical study of the long time behaviour of dispersive shock waves in solutions to the Kadomtsev–Petviashvili (KP) I equation is presented. It is shown that modulated lump solutions emerge from the dispersive shock waves. For the description of dispersive shock waves, Whitham modulation equations for KP are obtained.
Dispersive shock waves
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WebThe instability properties of the dark soliton are directly related to those of oblique dispersive shock wave (DSW) solutions. Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of … WebIn dispersive media, hydrodynamic singularities are resolved by coherent wavetrains known as dispersive shock waves (DSWs). Only dynamically expanding, temporal DSWs are possible in one-dimensional media. The additional degree of freedom inherent in two-dimensional media allows for the generation of time-independent DSWs that exhibit …
WebThis occurs because the shock wave is a nonlinearly steepened dispersive fast/magnetosonic wave (which happens to be a compressive version of a whistler mode wave under the right conditions). The dispersive nature of the magnetosonic-whistler wave is such that smaller (larger) wavelengths (frequencies) propagate faster than the converse. WebMar 30, 2024 · Shock waves are nonlinear structures characterized by a discontinuous jump in the wave profile. There exist prototypical examples of partial differential equations (PDEs), including the well-known Burgers’ equation (without dissipation), where the relevant waveforms feature infinite derivatives arising in finite time.
WebDec 1, 2007 · Individual dispersive shock waves (DSWs), characterized by expanding, modulated, periodic 1-phase waves, have been well-studied theoretically , , , , ; a detailed understanding of multiphase waves and DSW interactions in particular, is still lacking. In this work, we present a theory of dispersive shock wave interactions. Dispersive shock waves (DSWs) are fascinating wave phenomena occurring in media when nonlinearity overwhelms dispersion (or diffraction). Creating DSWs with low generation power and realizing their active controls is desirable but remains a longstanding challenge. Here, we propose a scheme to generate weak-light DSWs and realize their manipulations in an atomic gas involving strongly ...
WebOct 15, 2016 · 1. Introduction. In recent years the study of dispersive shock waves (DSWs) has generated considerable interest. In water waves DSWs have also been termed undular bores [1], [2].In fact, an early observation of an undular bore goes back to 1850 [3].In plasma physics a careful observation of a DSW, sometimes referred to as a …
WebWhen the flux is convex, the combination of diffusion and dispersion is known to give rise to monotonic and oscillatory traveling waves that approximate shock waves. The zero-diffusion limits of these traveling waves are dynamically expanding dispersive shock waves (DSWs). A richer set of wave solutions can be found when the flux is nonconvex. pyhäjärvi tammelaWebNov 7, 2024 · A dispersive shock wave is characterized by an expanding, coherent nonlinear waveform with a trailing large amplitude soliton edge, rank-ordered interior oscillations, and a leading small ... pyhäjärviseudun ympäristöhuolto oyWebOct 15, 2016 · Dispersive shock waves (DSWs) are non-stationary wave trains that form spontaneously in weakly dispersive media [1]. The underlying mechanism is the wave steepening driven by the nonlinearity which leads to a gradient catastrophe, regularized by dispersion that becomes important close to the point where strong gradients are formed. ... pyhäjärvi karttaWebOct 15, 2016 · Dispersive shock waves in the KdV and cKdV equations In this section we will investigate the DSW solutions associated with both the KdV and cKdV equations via Whitham modulation theory. We will compare Whitham theory at leading order and direct numerical simulations and show that they agree well. pyhäjärvi-instituuttipyhäjärvi ul seurakuntaWebApr 12, 2024 · Under some constraints, we build exact and approximate first- and second-order rogue wave (RW) solutions with two control and one free parameters for a quasi-one-dimensional Gross–Pitaevskii (GP) equation with a time-varying interatomic interaction, an external trap and gain/loss term through the similarity transformation technique. … pyhäjärvi vplWebJan 7, 2024 · Dispersive shock waves (DSWs) are generated around the shock front for some conditions. It is also found that the period of the DSW decreases monotonically with the inward compressional speed of boundaries, more substantially than the time delay of shocks τ. When the inward compressional speed of boundaries increases further, the … pyhäjärviteatteri