In 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 contact discontinuities). One can see their definition for a general 2 × 2 system with fluxes linear in one of dependent variables in [8]. This paper is devoted t...

A full particle simulation study is carried out on the electron acceleration at a collisionless, relatively low Alfven Mach number (MA = 5), perpendicular shock. Recent self-consistent hybrid shock simulations have demonstrated that the shock front of perpendicular shocks has a dynamic rippled character along the shock surface of low-Mach-number perpendicular shocks. In this paper, the effect o...

The caustics of weak shock waves are studied through matched asymptotic expansions. It is shown that these caustics are thinner and more intense than those of smooth waves with a comparable amplitude. This difference in scalings solves a paradox that would have the caustics of weak shock waves behave linearly, even though linear theory for discontinuous fronts predicts infinite amplitudes near ...

This paper is devoted to the rigorous theory of nonlinear geometric optics for multiple shocks to a general N × N conservation law in one space variable. For the problem of multiple weak shocks perturbed by small amplitude, high-frequency oscillatory waves, we obtain that the leading profiles of oscillatory shocks are solution to an integro-differential system with free boundaries, the leading ...

Shock wave theory was studied in literature by many authors. This article presents a survey with references about various topics related to shock waves: Hyperbolic conservation laws, Well-posedness theory, Compactness theory, Shock and reaction-di¤usion wave, The CJ and ZND theory, Existence of detonation in Majda’s model, Premixed laminar ‡ame, Multidimensional gas ‡ows, Multidimensional Riema...

A coordinate transformation is found which diagonalizes the axisym-metric pp-waves. Its effect upon concrete solutions, including impulsive and shock waves, is discussed.

This paper describes some recent theoretical results pertaining to the experimentally-observed relation between the speed of a shock wave in a solid and the particle velocity immediately behind the shock. The new feature in the present analysis is the assumption that compressive strains are limited by a materially-determined critical value, and that the internal energy density characterizing th...

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We construct supersymmetric brane solutions in string and M-theory with moduli parameters that depend arbitrarily on the light-cone time. Our investigation aims in understanding time dependent phenomena in gauge theories at strong coupling within the gauge/gravity correspondence. For that reason we use, as a basic ingredient, multicenter supergravity solutions which model the Coulomb branch of ...

We experimentally investigate the interplay between spatial shock waves and the degree of disorder during nonlinear optical propagation in a thermal defocusing medium. We characterize the way the shock point is affected by the amount of disorder and scales with wave amplitude. Evidence for the existence of a phase diagram in terms of nonlinearity and amount of randomness is reported. The result...